text:
Skewness
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For the planarity measure in graph theory, see Graph skewness.
Example distribution with non-zero (positive) skewness. These data are from experiments on wheat grass growth.
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or undefined.
The qualitative interpretation of the skew is complicated and unintuitive. Skew does not refer to the direction the curve appears to be leaning; in fact, the opposite is true. For a unimodal distribution, negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the right side – it does not distinguish these two kinds of shape. Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but is also true for an asymmetric distribution where the asymmetries even out, such as one tail being long but thin, and the other being short but fat. Further, in multimodal distributions and discrete distributions, skewness is also difficult to interpret. Importantly, the skewness does not determine the relationship of mean and median. In cases where it is necessary, data might be transformed to have a normal distribution.
Contents
[hide]
1 Introduction
2 Relationship of mean and median
3 Definition
3.1 Pearson's moment coefficient of skewness
3.2 Examples
3.3 Properties
3.4 Sample skewness
4 Applications
5 Other measures of skewness
5.1 Pearson's first skewness coefficient (mode skewness)
5.2 Pearson's second skewness coefficient (median skewness)
5.3 Quantile-based measures
5.4 Groeneveld & Meeden’s coefficient
5.5 L-moments
5.6 Distance skewness
5.7 Medcouple
6 See also
7 Notes
8 References
9 External links
Introduction[edit]
Consider the two distributions in the figure just below. Within each graph, the values on the right side of the distribution taper differently from the values on the left side. These tapering sides are called tails, and they provide a visual means to determine which of the two kinds of skewness a distribution has:
negative skew: The left tail is longer; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data. A left-skewed distribution usually appears as a right-leaning curve.[1]
positive skew: The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve itself appears to be skewed or leaning to the left; right instead refers to the right tail being drawn out and, often, the mean being skewed to the right of a typical center of the data. A right-skewed distribution usually appears as a left-leaning curve.[1]
Skewness in a data series may sometimes be observed not only graphically but by simple inspection of the values. For instance, consider the numeric sequence (49, 50, 51), whose values are evenly distributed around a central value of 50. We can transform this sequence into a negatively skewed distribution by adding a value far below the mean, e.g. (40, 49, 50, 51). Similarly, we can make the sequence positively skewed by adding a value far above the mean, e.g. (49, 50, 51, 60).
Relationship of mean and median[edit]
The skewness is not directly related to the relationship between the mean and median: a distribution with negative skew can have its mean greater than or less than the median, and likewise for positive skew.
In the older notion of nonparametric skew, defined as ( μ − ν ) / σ , {\displaystyle (\mu -\nu )/\sigma ,} where µ is the mean, ν is the median, and σ is the standard deviation, the skewness is defined in terms of this relationship: positive/right nonparametric skew means the mean is greater than (to the right of) the median, while negative/left nonparametric skew means the mean is less than (to the left of) the median. However, the modern definition of skewness and the traditional nonparametric definition do not in general have the same sign: while they agree for some families of distributions, they differ in general, and conflating them is misleading.
If the distribution is symmetric, then the mean is equal to the median, and the distribution has zero skewness.[2] If, in addition, the distribution is unimodal, then the mean = median = mode. This is the case of a coin toss or the series 1,2,3,4,... Note, however, that the converse is not true in general, i.e. zero skewness does not imply that the mean is equal to the median.
Paul T. von Hippel points out: "Many textbooks, teach a rule of thumb stating that the mean is right of the median under right skew, and left of the median under left skew. This rule fails with surprising frequency. It can fail in multimodal distributions, or in distributions where one tail is long but the other is heavy. Most commonly, though, the rule fails in discrete distributions where the areas to the left and right of the median are not equal. Such distributions not only contradict the textbook relationship between mean, median, and skew, they also contradict the textbook interpretation of the median."[3]
Definition[edit]
Pearson's moment coefficient of skewness[edit]
The skewness of a random variable X is the third standardized moment γ1, defined as:[4][5]
γ 1 = E  [ ( X − μ σ ) 3 ] = μ 3 σ 3 = E  [ ( X − μ ) 3 ] ( E  [ ( X − μ ) 2 ] ) 3 / 2 = κ 3 κ 2 3 / 2 {\displaystyle \gamma _{1}=\operatorname {E} \left[\left({\frac {X-\mu }{\sigma }}\right)^{3}\right]={\frac {\mu _{3}}{\sigma ^{3}}}={\frac {\operatorname {E} \left[(X-\mu )^{3}\right]}{\ \ \ (\operatorname {E} \left[(X-\mu )^{2}\right])^{3/2}}}={\frac {\kappa _{3}}{\kappa _{2}^{3/2}}}}

where μ is the mean, σ is the standard deviation, E is the expectation operator, μ3 is the third central moment, and κt are the tth cumulants. It is sometimes referred to as Pearson's moment coefficient of skewness,[5] or simply the moment coefficient of skewness,[4] but should not be confused with Pearson's other skewness statistics (see below). The last equality expresses skewness in terms of the ratio of the third cumulant κ3 to the 1.5th power of the second cumulant κ2. This is analogous to the definition of kurtosis as the fourth cumulant normalized by the square of the second cumulant. The skewness is also sometimes denoted Skew[X].
Skewness can be expressed in terms of the non-central moment E[X3] by expanding the previous formula,
γ 1 = E  [ ( X − μ σ ) 3 ] = E  [ X 3 ] − 3 μ E  [ X 2 ] + 3 μ 2 E  [ X ] − μ 3 σ 3 = E  [ X 3 ] − 3 μ ( E  [ X 2 ] − μ E  [ X ] ) − μ 3 σ 3 = E  [ X 3 ] − 3 μ σ 2 − μ 3 σ 3 . {\displaystyle {\begin{aligned}\gamma _{1}&=\operatorname {E} \left[\left({\frac {X-\mu }{\sigma }}\right)^{3}\right]\\&={\frac {\operatorname {E} [X^{3}]-3\mu \operatorname {E} [X^{2}]+3\mu ^{2}\operatorname {E} [X]-\mu ^{3}}{\sigma ^{3}}}\\&={\frac {\operatorname {E} [X^{3}]-3\mu (\operatorname {E} [X^{2}]-\mu \operatorname {E} [X])-\mu ^{3}}{\sigma ^{3}}}\\&={\frac {\operatorname {E} [X^{3}]-3\mu \sigma ^{2}-\mu ^{3}}{\sigma ^{3}}}.\end{aligned}}}
Examples[edit]
Skewness can be infinite, as when
Pr [ X > x ] = x − 2 for x > 1 , Pr [ X < 1 ] = 0 {\displaystyle \Pr \left[X>x\right]=x^{-2}{\mbox{ for }}x>1,\ \Pr[X<1]=0}
where the third cumulants are infinite, or as when
Pr [ X < x ] = ( 1 − x ) − 3 / 2 for negative x and Pr [ X > x ] = ( 1 + x ) − 3 / 2 for positive x . {\displaystyle \Pr[X<x]=(1-x)^{-3}/2{\mbox{ for negative }}x{\mbox{ and }}\Pr[X>x]=(1+x)^{-3}/2{\mbox{ for positive }}x.}
where the third cumulant is undefined.
Properties[edit]
Starting from a standard cumulant expansion around a normal distribution, one can show that
skewness = 6 (mean − median)/standard deviation (1 + kurtosis/8) + O (skewness2).[citation needed]
If Y is the sum of n independent and identically distributed random variables, all with the distribution of X, then the third cumulant of Y is n times that of X and the second cumulant of Y is n times that of X, so Skew [ Y ] = Skew [ X ] / n {\displaystyle {\mbox{Skew}}[Y]={\mbox{Skew}}[X]/{\sqrt {n}}} . This shows that the skewness of the sum is smaller, as it approaches a Gaussian distribution in accordance with the central limit theorem. Note that the assumption that the variables be independent for the above formula is very important because it is possible even for the sum of two Gaussian variables to have a skewed distribution (see this example).
Sample skewness[edit]
For a sample of n values, a natural method of moments estimator of the population skewness is[6]
b 1 = m 3 s 3 = 1 n ∑ i = 1 n ( x i − x ¯ ) 3 1 n − 1 ∑ i = 1 n ( x i − x ¯ ) 2 3 = 1 n ∑ i = 1 n ( x i − x ¯ ) 3 [ 1 n − 1 ∑ i = 1 n ( x i − x ¯ ) 2 ] 3 / 2 , {\displaystyle b_{1}={\frac {m_{3}}{s^{3}}}={\frac {{\tfrac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\overline {x}})^{3}}{{\sqrt {{\tfrac {1}{n-1}}\sum _{i=1}^{n}(x_{i}-{\overline {x}})^{2}}}^{\,3}}}={\frac {{\tfrac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\overline {x}})^{3}}{\left[{\tfrac {1}{n-1}}\sum _{i=1}^{n}(x_{i}-{\overline {x}})^{2}\right]^{3/2}}}\ ,}

where x ¯ {\displaystyle {\overline {x}}} is the sample mean, s is the sample standard deviation, and the numerator m3 is the sample third central moment.
Another common definition of the sample skewness is[6]
G 1 = k 3 k 2 3 / 2 = n 2 ( n − 1 ) ( n − 2 ) m 3 s 3 , {\displaystyle G_{1}={\frac {k_{3}}{k_{2}^{3/2}}}={\frac {n^{2}}{(n-1)(n-2)}}\;{\frac {m_{3}}{s^{3}}},}
where k 3 {\displaystyle k_{3}} is the unique symmetric unbiased estimator of the third cumulant and k 2 = s 2 {\displaystyle k_{2}=s^{2}} is the symmetric unbiased estimator of the second cumulant (i.e. the variance).
In general, the ratios b 1 {\displaystyle b_{1}} and G 1 {\displaystyle G_{1}} are both biased estimators of the population skewness γ 1 {\displaystyle \gamma _{1}} ; their expected values can even have the opposite sign from the true skewness. (For instance, a mixed distribution consisting of very thin Gaussians centred at −99, 0.5, and 2 with weights 0.01, 0.66, and 0.33 has a skewness of about −9.77, but in a sample of 3, G 1 {\displaystyle G_{1}} has an expected value of about 0.32, since usually all three samples are in the positive-valued part of the distribution, which is skewed the other way.) Nevertheless, b 1 {\displaystyle b_{1}} and G 1 {\displaystyle G_{1}} each have obviously the correct expected value of zero for any symmetric distribution with a finite third moment, including a normal distribution.
Under the assumption that the underlying random variable X {\displaystyle X} is normally distributed, it can be shown that n b 1 → d N ( 0 , 6 ) {\displaystyle {\sqrt {n}}b_{1}{\xrightarrow {d}}N(0,6)} . The variance of the skewness of a random sample of size n from a normal distribution is[7][8]
var  ( G 1 ) = 6 n ( n − 1 ) ( n − 2 ) ( n + 1 ) ( n + 3 ) . {\displaystyle \operatorname {var} (G_{1})={\frac {6n(n-1)}{(n-2)(n+1)(n+3)}}.}
An approximate alternative is 6/n, but this is inaccurate for small samples.
In normal samples, b 1 {\displaystyle b_{1}} has the smaller variance of the two estimators, with
var  ( b 1 ) < var  ( m 3 m 2 3 / 2 ) < var  ( G 1 ) , {\displaystyle \operatorname {var} (b_{1})<\operatorname {var} \left({\frac {m_{3}}{m_{2}^{3/2}}}\right)<\operatorname {var} (G_{1}),}
where m2 in the denominator is the (biased) sample second central moment.[6]
The adjusted Fisher–Pearson standardized moment coefficient G 1 {\displaystyle G_{1}} is the version found in Excel and several statistical packages including Minitab, SAS and SPSS.[9]
Applications[edit]
Skewness has few benefits as it is not often used in statistical analysis. Aside from indicating which direction and a relative magnitude of how far a distribution deviates from normal, skewness itself offers few analytical insights I.E. aside from calculating skewness for its own sake it is rarely if ever used as a variable in further calculations.
Many models assume normal distribution; i.e., data are symmetric about the mean. The normal distribution has a skewness of zero. But in reality, data points may not be perfectly symmetric. So, an understanding of the skewness of the dataset indicates whether deviations from the mean are going to be positive or negative.
D'Agostino's K-squared test is a goodness-of-fit normality test based on sample skewness and sample kurtosis.
Other measures of skewness[edit]
Comparison of mean, median and mode of two log-normal distributions with different skewnesses.
Other measures of skewness have been used, including simpler calculations suggested by Karl Pearson[10] (not to be confused with Pearson's moment coefficient of skewness, see above). These other measures are:
Pearson's first skewness coefficient (mode skewness)[edit]
The Pearson mode skewness,[11] or first skewness coefficient, is defined as
mean − mode/standard deviation.
Pearson's second skewness coefficient (median skewness)[edit]
The Pearson median skewness, or second skewness coefficient,[12][13] is defined as
3 (mean − median)/standard deviation.
The latter is a simple multiple of the nonparametric skew.
Quantile-based measures[edit]
Bowley's measure of skewness (from 1901),[14][15] also called Yule's coefficient (from 1912)[16][17] is defined as:
B 1 = Q 3 + Q 1 − 2 Q 2 Q 3 − Q 1 {\displaystyle B_{1}={\frac {{{Q}_{3}}+{{Q}_{1}}-2{{Q}_{2}}}{{{Q}_{3}}-{{Q}_{1}}}}} .
When writing it as Q 3 + Q 1 2 − Q 2 Q 3 − Q 1 2 {\displaystyle {\frac {{\frac {{{Q}_{3}}+{{Q}_{1}}}{2}}-{{Q}_{2}}}{\frac {{{Q}_{3}}-{{Q}_{1}}}{2}}}} , it is easier to see that the numerator is the average of the upper and lower quartiles (a measure of location) minus the median while the denominator is (Q3-Q1)/2 which (for symmetric distributions) is the MAD measure of dispersion.
Other names for this measure are Galton's measure of skewness,[18] the Yule–Kendall index[19] and the quartile skewness[citation needed],
A more general formulation of a skewness function was described by Groeneveld, R. A. and Meeden, G. (1984):[20][21][22]
γ ( u ) = F − 1 ( u ) + F − 1 ( 1 − u ) − 2 F − 1 ( 1 / 2 ) F − 1 ( u ) − F − 1 ( 1 − u ) {\displaystyle \gamma (u)={\frac {F^{-1}(u)+F^{-1}(1-u)-2F^{-1}(1/2)}{F^{-1}(u)-F^{-1}(1-u)}}}
where F is the cumulative distribution function. This leads to a corresponding overall measure of skewness[21] defined as the supremum of this over the range 1/2 ≤ u < 1. Another measure can be obtained by integrating the numerator and denominator of this expression.[20] The function γ(u) satisfies −1 ≤ γ(u) ≤ 1 and is well defined without requiring the existence of any moments of the distribution.[20]
Bowley's measure of skewness is γ(u) evaluated at u = 3/4. Kelley's measure of skewness uses u = 0.1.[citation needed]
Groeneveld & Meeden’s coefficient[edit]
Groeneveld & Meeden have suggested, as an alternative measure of skewness,[20]
B 3 = s k e w ( X ) = ( μ − ν ) E ( | X − ν | ) , {\displaystyle B_{3}=\mathrm {skew} (X)={\frac {(\mu -\nu )}{E(|X-\nu |)}},}
where μ is the mean, ν is the median, |…| is the absolute value, and E() is the expectation operator. This is closely related in form to Pearson's second skewness coefficient.
L-moments[edit]
Use of L-moments in place of moments provides a measure of skewness known as the L-skewness.[23]
Distance skewness[edit]
A value of skewness equal to zero does not imply that the probability distribution is symmetric. Thus there is a need for another measure of asymmetry that has this property: such a measure was introduced in 2000.[24] It is called distance skewness and denoted by dSkew. If X is a random variable taking values in the d-dimensional Euclidean space, X has finite expectation, X' is an independent identically distributed copy of X, and ∥ ⋅ ∥ {\displaystyle \|\cdot \|} denotes the norm in the Euclidean space, then a simple measure of asymmetry is
dSkew  ( X ) := 1 − E  ∥ X − X ′ ∥ E  ∥ X + X ′ ∥ if Pr ( X = 0 ) ≠ 1 {\displaystyle \operatorname {dSkew} (X):=1-{\frac {\operatorname {E} \|X-X'\|}{\operatorname {E} \|X+X'\|}}{\text{ if }}\Pr(X=0)\neq 1}
and dSkew(X) := 0 for X = 0 (with probability 1). Distance skewness is always between 0 and 1, equals 0 if and only if X is diagonally symmetric (X and −X have the same probability distribution) and equals 1 if and only if X is a nonzero constant with probability one.[25] Thus there is a simple consistent statistical test of diagonal symmetry based on the sample distance skewness:
dSkew n  ( X ) := 1 − ∑ i , j ∥ x i − x j ∥ ∑ i , j ∥ x i + x j ∥ . {\displaystyle \operatorname {dSkew} _{n}(X):=1-{\frac {\sum _{i,j}\|x_{i}-x_{j}\|}{\sum _{i,j}\|x_{i}+x_{j}\|}}.}
Medcouple[edit]
The medcouple is a scale-invariant robust measure of skewness, with a breakdown point of 25%.[26] It is the median of the values of the kernel function
h ( x i , x j ) = ( x i − x m ) − ( x m − x j ) x i − x j {\displaystyle h(x_{i},x_{j})={\frac {(x_{i}-x_{m})-(x_{m}-x_{j})}{x_{i}-x_{j}}}}
taken over all couples ( x i , x j ) {\displaystyle (x_{i},x_{j})} such that x i ≥ x m ≥ x j {\displaystyle x_{i}\geq x_{m}\geq x_{j}} , where x m {\displaystyle x_{m}} is the median of the sample { x 1 , x 2 , … , x n } {\displaystyle \{x_{1},x_{2},\ldots ,x_{n}\}} . It can be seen as the median of all possible quantile skewness measures.
See also[edit]
Wikimedia Commons has media related to Skewness (statistics).
Bragg peak
Coskewness
Shape parameters
Skew normal distribution
Skewness risk
Notes[edit]
^ Jump up to: a b Susan Dean, Barbara Illowsky "Descriptive Statistics: Skewness and the Mean, Median, and Mode", Connexions website
Jump up ^ "1.3.5.11. Measures of Skewness and Kurtosis". NIST. Retrieved 18 March 2012.
Jump up ^ von Hippel, Paul T. (2005). "Mean, Median, and Skew: Correcting a Textbook Rule". Journal of Statistics Education. 13 (2).
^ Jump up to: a b "Measures of Shape: Skewness and Kurtosis", 2008–2016 by Stan Brown, Oak Road Systems
^ Jump up to: a b Pearson's moment coefficient of skewness, FXSolver.com
^ Jump up to: a b c Joanes, D. N.; Gill, C. A. (1998). "Comparing measures of sample skewness and kurtosis". Journal of the Royal Statistical Society (Series D): The Statistician. 47 (1): 183–189. doi:10.1111/1467-9884.00122.
Jump up ^ Duncan Cramer (1997) Fundamental Statistics for Social Research. Routledge. ISBN 9780415172042 (p 85)
Jump up ^ Kendall, M.G.; Stuart, A. (1969) The Advanced Theory of Statistics, Volume 1: Distribution Theory, 3rd Edition, Griffin. ISBN 0-85264-141-9 (Ex 12.9)
Jump up ^ Doane DP, Seward LE (2011) J Stat Educ 19 (2)
Jump up ^ http://www.stat.upd.edu.ph/s114%20cnotes%20fcapistrano/Chapter%2010.pdf
Jump up ^ Weisstein, Eric W. "Pearson Mode Skewness". MathWorld.
Jump up ^ Weisstein, Eric W. "Pearson's skewness coefficients". MathWorld.
Jump up ^ Doane, David P., and Lori E. Seward. "Measuring Skewness: A Forgotten Statistic?" Journal of Statistics Education 19.2 (2011): 1-18.
Jump up ^ Bowley, A. L. (1901). Elements of Statistics, P.S. King & Son, Laondon. Or in a later edition: BOWLEY, AL. "Elements of Statistics, 4th Edn (New York, Charles Scribner)."(1920).
Jump up ^ Kenney JF and Keeping ES (1962) Mathematics of Statistics, Pt. 1, 3rd ed., Van Nostrand, (page 102).
Jump up ^ Yule, George Udny. An introduction to the theory of statistics. C. Griffin, limited, 1912.
Jump up ^ Groeneveld, Richard A. "An influence function approach to describing the skewness of a distribution." The American Statistician 45.2 (1991): 97-102.
Jump up ^ Johnson et al (1994) p 3, p 40
Jump up ^ Wilks DS (1995) Statistical Methods in the Atmospheric Sciences, p 27. Academic Press. ISBN 0-12-751965-3
^ Jump up to: a b c d Groeneveld, R.A.; Meeden, G. (1984). "Measuring Skewness and Kurtosis". The Statistician. 33 (4): 391–399. JSTOR 2987742. doi:10.2307/2987742.
^ Jump up to: a b MacGillivray (1992)
Jump up ^ Hinkley DV (1975) "On power transformations to symmetry", Biometrika, 62, 101–111
Jump up ^ Hosking, J.R.M. (1992). "Moments or L moments? An example comparing two measures of distributional shape". The American Statistician. 46 (3): 186–189. JSTOR 2685210. doi:10.2307/2685210.
Jump up ^ Szekely, G.J. (2000). "Pre-limit and post-limit theorems for statistics", In: Statistics for the 21st Century (eds. C. R. Rao and G. J. Szekely), Dekker, New York, pp. 411–422.
Jump up ^ Szekely, G. J. and Mori, T. F. (2001) "A characteristic measure of asymmetry and its application for testing diagonal symmetry", Communications in Statistics – Theory and Methods 30/8&9, 1633–1639.
Jump up ^ G. Brys; M. Hubert; A. Struyf (November 2004). "A Robust Measure of Skewness". Journal of Computational and Graphical Statistics. 13 (4): 996–1017. doi:10.1198/106186004X12632.
Premaratne, G., Bera, A. K. (2001).
Adjusting the Tests for Skewness and Kurtosis for Distributional Misspecifications. Working Paper Number 01-0116, University of Illinois. Forthcoming in Comm in Statistics, Simulation and Computation.2016 1-15
Premaratne, G., Bera, A. K. (2000). Modeling Asymmetry and Excess Kurtosis in Stock Return Data. Office of Research Working Paper Number 00-0123, University of Illinois
References[edit]
Johnson, NL, Kotz, S, Balakrishnan N (1994) Continuous Univariate Distributions, Vol 1, 2nd Edition Wiley ISBN 0-471-58495-9
MacGillivray, HL (1992). "Shape properties of the g- and h- and Johnson families". Comm. Statistics — Theory and Methods. 21: 1244–1250.
Skewness Measures for the Weibull Distribution
External links[edit]
Wikiversity has learning resources about Skewness
Hazewinkel, Michiel, ed. (2001) [1994], "Asymmetry coefficient", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
An Asymmetry Coefficient for Multivariate Distributions by Michel Petitjean
On More Robust Estimation of Skewness and Kurtosis Comparison of skew estimators by Kim and White.
Closed-skew Distributions — Simulation, Inversion and Parameter Estimation
[hide]
v
t
e
Statistics
Outline
Index
[hide]
Descriptive statistics
Continuous data
Center
Mean
arithmetic
geometric
harmonic
Median
Mode
Dispersion
Variance
Standard deviation
Coefficient of variation
Percentile
Range
Interquartile range
Shape
Central limit theorem
Moments
Skewness
Kurtosis
L-moments
Count data
Index of dispersion
Summary tables
Grouped data
Frequency distribution
Contingency table
Dependence
Pearson product-moment correlation
Rank correlation
Spearman's rho
Kendall's tau
Partial correlation
Scatter plot
Graphics
Bar chart
Biplot
Box plot
Control chart
Correlogram
Fan chart
Forest plot
Histogram
Pie chart
Q–Q plot
Run chart
Scatter plot
Stem-and-leaf display
Radar chart
[show]
Data collection
Study design
Population
Statistic
Effect size
Statistical power
Sample size determination
Missing data
Survey methodology
Sampling
stratified
cluster
Standard error
Opinion poll
Questionnaire
Controlled experiments
Design
control
optimal
Controlled trial
Randomized
Random assignment
Replication
Blocking
Interaction
Factorial experiment
Uncontrolled studies
Observational study
Natural experiment
Quasi-experiment
[show]
Statistical inference
Statistical theory
Population
Statistic
Probability distribution
Sampling distribution
Order statistic
Empirical distribution
Density estimation
Statistical model
Lp space
Parameter
location
scale
shape
Parametric family
Likelihood (monotone)
Location–scale family
Exponential family
Completeness
Sufficiency
Statistical functional
Bootstrap
U
V
Optimal decision
loss function
Efficiency
Statistical distance
divergence
Asymptotics
Robustness
Frequentist inference
Point estimation
Estimating equations
Maximum likelihood
Method of moments
M-estimator
Minimum distance
Unbiased estimators
Mean-unbiased minimum-variance
Rao–Blackwellization
Lehmann–Scheffé theorem
Median unbiased
Plug-in
Interval estimation
Confidence interval
Pivot
Likelihood interval
Prediction interval
Tolerance interval
Resampling
Bootstrap
Jackknife
Testing hypotheses
1- & 2-tails
Power
Uniformly most powerful test
Permutation test
Randomization test
Multiple comparisons
Parametric tests
Likelihood-ratio
Wald
Score
Specific tests
Z (normal)
Student's t-test
F
Goodness of fit
Chi-squared
Kolmogorov–Smirnov
Anderson–Darling
Lilliefors
Jarque–Bera
Normality (Shapiro–Wilk)
Likelihood-ratio test
Model selection
Cross validation
AIC
BIC
Rank statistics
Sign
Sample median
Signed rank (Wilcoxon)
Hodges–Lehmann estimator
Rank sum (Mann–Whitney)
Nonparametric anova
1-way (Kruskal–Wallis)
2-way (Friedman)
Ordered alternative (Jonckheere–Terpstra)
Bayesian inference
Bayesian probability
prior
posterior
Credible interval
Bayes factor
Bayesian estimator
Maximum posterior estimator
[show]
Correlation
Regression analysis
Correlation
Pearson product-moment
Partial correlation
Confounding variable
Coefficient of determination
Regression analysis
Errors and residuals
Regression model validation
Mixed effects models
Simultaneous equations models
Multivariate adaptive regression splines (MARS)
Linear regression
Simple linear regression
Ordinary least squares
General linear model
Bayesian regression
Non-standard predictors
Nonlinear regression
Nonparametric
Semiparametric
Isotonic
Robust
Heteroscedasticity
Homoscedasticity
Generalized linear model
Exponential families
Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance
Analysis of variance (ANOVA, anova)
Analysis of covariance
Multivariate ANOVA
Degrees of freedom
[show]
Categorical / Multivariate / Time-series / Survival analysis
Categorical
Cohen's kappa
Contingency table
Graphical model
Log-linear model
McNemar's test
Multivariate
Regression
Manova
Principal components
Canonical correlation
Discriminant analysis
Cluster analysis
Classification
Structural equation model
Factor analysis
Multivariate distributions
Elliptical distributions
Normal
Time-series
General
Decomposition
Trend
Stationarity
Seasonal adjustment
Exponential smoothing
Cointegration
Structural break
Granger causality
Specific tests
Dickey–Fuller
Johansen
Q-statistic (Ljung–Box)
Durbin–Watson
Breusch–Godfrey
Time domain
Autocorrelation (ACF)
partial (PACF)
Cross-correlation (XCF)
ARMA model
ARIMA model (Box–Jenkins)
Autoregressive conditional heteroskedasticity (ARCH)
Vector autoregression (VAR)
Frequency domain
Spectral density estimation
Fourier analysis
Wavelet
Survival
Survival function
Kaplan–Meier estimator (product limit)
Proportional hazards models
Accelerated failure time (AFT) model
First hitting time
Hazard function
Nelson–Aalen estimator
Test
Log-rank test
[show]
Applications
Biostatistics
Bioinformatics
Clinical trials / studies
Epidemiology
Medical statistics
Engineering statistics
Chemometrics
Methods engineering
Probabilistic design
Process / quality control
Reliability
System identification
Social statistics
Actuarial science
Census
Crime statistics
Demography
Econometrics
National accounts
Official statistics
Population statistics
Psychometrics
Spatial statistics
Cartography
Environmental statistics
Geographic information system
Geostatistics
Kriging
Category
Portal
Commons
WikiProject
Retrieved from "https://en.wikipedia.org/w/index.php?title=Skewness&oldid=806429050"
Categories:
Moment (mathematics)
Statistical deviation and dispersion
Hidden categories:
Use dmy dates from July 2012
All articles with unsourced statements
Articles with unsourced statements from April 2010
Articles with unsourced statements from February 2016
Articles with unsourced statements from January 2012
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
Беларуская
Català
Čeština
Deutsch
Eesti
Español
Euskara
فارسی
Français
한국어
Italiano
עברית
Latviešu
Lietuvių
Magyar
Македонски
Nederlands
日本語
Norsk
Polski
Português
Русский
Slovenčina
Slovenščina
Basa Sunda
Suomi
Svenska
తెలుగు
Türkçe
Українська
Tiếng Việt
中文
Edit links
This page was last edited on 22 October 2017, at 00:03.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

values:
/wiki/Graph_skewness
mw-redirect
Graph skewness

values:
note
hatnote navigation-not-searchable

attrs: class style

value: b

values: Negative and positive skew diagrams (English).svg

values: Edit section: Relationship of mean and median

values: vertical-align: -0.838ex; width:10.506ex; height:2.843ex;

values:
/wiki/Unimodal_distribution
mw-redirect
Unimodal distribution

values: Edit section: Pearson's moment coefficient of skewness

values: vertical-align: -3.505ex; width:58.028ex; height:7.843ex;

attrs: columnalign rowspacing columnspacing displaystyle

values: right left right left right left right left right left right left

values: 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em

values: vertical-align: -12.671ex; width:41.857ex; height:26.509ex;

values: vertical-align: -0.838ex; width:43.45ex; height:3.176ex;

values: vertical-align: -0.838ex; width:84.773ex; height:3.176ex;

values: display:block; line-height:1em; margin:0 0.1em;

values: display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;

values: display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;

values: This claim needs references to reliable sources. (April 2010)

values:
noprint Inline-Template Template-Fact
white-space:nowrap;

values: Independent and identically distributed random variables

values: vertical-align: -1.005ex; width:24.581ex; height:3.009ex;

values: vertical-align: -5.171ex; width:65.102ex; height:9.676ex;

values: vertical-align: -0.338ex; width:1.455ex; height:2.509ex;

values:
/wiki/Sample_mean
mw-redirect
Sample mean

values: vertical-align: -3.505ex; width:34.5ex; height:7.343ex;

values: vertical-align: -0.671ex; width:2.283ex; height:2.509ex;

values: vertical-align: -0.671ex; width:7.555ex; height:3.009ex;

values: vertical-align: -0.671ex; width:2.07ex; height:2.509ex;

values: vertical-align: -0.671ex; width:2.899ex; height:2.509ex;

values: vertical-align: -0.838ex; width:2.276ex; height:2.176ex;

values: vertical-align: -0.338ex; width:1.99ex; height:2.176ex;

values: vertical-align: -1.005ex; margin-top: -0.442ex; width:15.05ex; height:4.509ex;

values: {\displaystyle {\sqrt {n}}b_{1}{\xrightarrow {d}}N(0,6)}

values: vertical-align: -2.671ex; width:34.442ex; height:6.509ex;

values: vertical-align: -3.505ex; width:34.812ex; height:7.843ex;

values: Edit section: Other measures of skewness

values: Edit section: Pearson's first skewness coefficient (mode skewness)

values: Edit section: Pearson's second skewness coefficient (median skewness)

values: vertical-align: -2.505ex; width:22.387ex; height:6.176ex;

values: vertical-align: -4.005ex; width:13.009ex; height:9.176ex;

values: This claim needs references to reliable sources. (February 2016)

values: vertical-align: -2.671ex; width:43.494ex; height:6.676ex;

values: This claim needs references to reliable sources. (January 2012)

values: Edit section: Groeneveld & Meeden’s coefficient

values: vertical-align: -2.671ex; width:30.279ex; height:6.509ex;

values: vertical-align: -0.838ex; width:4.035ex; height:2.843ex;

values: vertical-align: -2.671ex; width:48.717ex; height:6.509ex;

values:
/wiki/Statistical_test
mw-redirect
Statistical test

values: vertical-align: -3.171ex; width:35.314ex; height:7.509ex;

values:
/wiki/Breakdown_point
mw-redirect
Breakdown point

values: vertical-align: -2.505ex; width:35.236ex; height:6.509ex;

values: vertical-align: -1.005ex; width:7.279ex; height:3.009ex;

values: vertical-align: -1.005ex; width:13.645ex; height:2.843ex;

values: vertical-align: -0.671ex; width:3.023ex; height:2.009ex;

values: vertical-align: -0.838ex; width:15.969ex; height:2.843ex;

values:
nofollow
http://cnx.org/content/m17104/latest/
external text

values:
nofollow
external text
http://brownmath.com/stat/shape.htm

values: Journal of the Royal Statistical Society

values:
nofollow
external text
//www.jstor.org/stable/2987742

values:
nofollow
external text
//doi.org/10.2307%2F2987742

values:
nofollow
external text
//www.jstor.org/stable/2685210

values:
nofollow
external text
//doi.org/10.2307%2F2685210

values:
nofollow
external text
//doi.org/10.1198%2F106186004X12632

values:
nofollow
external text
http://dahoiv.net/master/index.html

values:
/wiki/Shape_of_the_distribution
mw-redirect
Shape of the distribution

values: Pearson product-moment correlation coefficient

values: Kendall tau rank correlation coefficient

values: nowraplinks collapsible uncollapsed navbox-subgroup

values:
/wiki/Population_(statistics)
mw-redirect
Population (statistics)

values: nowraplinks collapsible collapsed navbox-subgroup

values:
/wiki/Maximum_likelihood
mw-redirect
Maximum likelihood

values:
/wiki/Median-unbiased_estimator
mw-redirect
Median-unbiased estimator

values:
/wiki/Likelihood_interval
mw-redirect
Likelihood interval

values:
/wiki/Power_(statistics)
mw-redirect
Power (statistics)

values:
/wiki/Permutation_test
mw-redirect
Permutation test

values:
/wiki/Randomization_test
mw-redirect
Randomization test

values:
/wiki/Multiple_comparisons
mw-redirect
Multiple comparisons

values:
/wiki/Rank_statistics
mw-redirect
Rank statistics

values:
/wiki/Sample_median
mw-redirect
Sample median

values: Kruskal–Wallis one-way analysis of variance

values:
CorrelationRegression_analysis
font-size:114%;margin:0 4em
hlist hlist-separated

values:
/wiki/Regression_model_validation
mw-redirect
Regression model validation

values: Multivariate adaptive regression splines

values:
/wiki/Multivariate_distribution
mw-redirect
Multivariate distribution

values:
/wiki/Trend_estimation
mw-redirect
Trend estimation

values: List of fields of application of statistics

values: nowraplinks hlist collapsible uncollapsed navbox-inner

values: navigation navbox Statistics padding:3px

values: Category:Statistical deviation and dispersion

values: Category:All articles with unsourced statements

values: Category:Articles with unsourced statements from April 2010

values: Category:Articles with unsourced statements from February 2016

values: Category:Articles with unsourced statements from January 2012

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Skewness
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values:
/w/index.php?title=Skewness&action=edit
Edit this page [ctrl-alt-e]
e

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values:
uls-settings-trigger
Language settings
0
button
true

values: Каэфіцыент асіметрыі – Belarusian

values: צידוד (סטטיסטיקה) – Hebrew

values: Коефициент на асиметрија – Macedonian

values:
https://no.wikipedia.org/wiki/Skjevhet
Skjevhet – Norwegian
no
no
interlanguage-link-target

values: Коэффициент асимметрии – Russian

values:
https://su.wikipedia.org/wiki/Skewness
Skewness – Sundanese
su
su
interlanguage-link-target

values:
https://fi.wikipedia.org/wiki/Vinous
Vinous – Finnish
fi
fi
interlanguage-link-target

values:
https://sv.wikipedia.org/wiki/Skevhet
Skevhet – Swedish
sv
sv
interlanguage-link-target

values: అసౌష్ఠవత – Telugu

values: Коефіцієнт асиметрії – Ukrainian

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Skewness rootpage-Skewness vector-experimental-print-styles vector-nav-directionality skin-vector action-view


text:
Rift valley
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Not to be confused with Rift zone.
For other uses, see Rift valley (disambiguation).
African Rift Valley. From left to right: Lake Upemba, Lake Mweru, Lake Tanganyika (largest), and Lake Rukwa.
A rift valley near Quilotoa, Ecuador.
The Ottawa-Bonnechere Graben
Þingvallavatn
A rift valley is a linear-shaped lowland between several highlands or mountain ranges created by the action of a geologic rift or fault. A rift valley is formed on a divergent plate boundary, a crustal extension or spreading apart of the surface,which is subsequently further deepened by the forces of erosion. When the tensional forces are strong enough to cause the plate to split apart, a center block drops between the two blocks at its flanks, forming a graben. The drop of the center creates the nearly parallel steeply dipping walls of a rift valley when it is new. That feature is the beginning of the rift valley, but as the process continues, the valley widens, until it becomes a large basin that fills with sediment from the rift walls and the surrounding area. One of the best known examples of this process is the East African Rift.[1] On Earth, rifts can occur at all elevations, from the sea floor to plateaus and mountain ranges in continental crust or in oceanic crust. They are often associated with a number of adjoining subsidiary or co-extensive valleys, which are typically considered part of the principal rift valley geologically.
Contents
1 Earth's rift valleys
1.1 Rift valley lakes
2 Extraterrestrial rift valleys
3 References
4 Further reading
Earth's rift valleys[edit]
The most extensive rift valley is located along the crest of the mid-ocean ridge system and is the result of sea floor spreading. Examples of this type of rift include the Mid-Atlantic Ridge and the East Pacific Rise.
Many existing continental rift valleys are the result of a failed arm (aulacogen) of a triple junction, although there are two, the East African Rift and the Baikal Rift Zone, which are currently active, as well as a third which may be, the West Antarctic Rift. In these instances, not only the crust, but also entire tectonic plates, are in the process of breaking apart to create new plates. If they continue, continental rifts will eventually become oceanic rifts.
Other rift valleys are the result of bends or discontinuities in horizontally-moving (strike-slip) faults. When these bends or discontinuities are in the same direction as the relative motions along the fault, extension occurs. For example, for a right lateral-moving fault, a bend to the right will result in stretching and consequent subsidence in the area of the irregularity. In the view of many geologists today, the Dead Sea lies in a rift which results from a leftward discontinuity in the left lateral-moving Dead Sea Transform fault. Where a fault breaks into two strands, or two faults run close to each other, crustal extension may also occur between them, as a result of differences in their motions. Both types of fault-caused extension commonly occur on a small scale, producing such features as sag ponds or landslides.
Rift valley lakes[edit]
Main article: Rift lake
Many of the world's largest lakes are located in rift valleys.[2] Lake Baikal in Siberia, a World Heritage Site,[3] lies in an active rift valley. Baikal is both the deepest lake in the world and, with 20% of all of the liquid freshwater on earth, has the greatest volume.[4] Lake Tanganyika, second by both measures, is in the Albertine Rift, the westernmost arm of the active East African Rift. Lake Superior in North America, the largest freshwater lake by area, lies in the ancient and dormant Midcontinent Rift. The largest subglacial lake, Lake Vostok, may also lie in an ancient rift valley.[5] Lake Nipissing and Lake Timiskaming in Ontario and Quebec, Canada lie inside a rift valley called the Ottawa-Bonnechere Graben.[6] Þingvallavatn, Iceland's largest natural lake, is also an example of a rift lake.
Extraterrestrial rift valleys[edit]
Extraterrestrial rift valleys are also known to occur on other terrestrial planets and natural satellites. The 4,000 km long Valles Marineris on Mars is believed by planetary geologists to be a large rift system.[7][8] Some features of Venus, most notably, the 4,000 km Devana Chasma[9] and a part of the western Eistla, and possibly also Alta and Bell Regio have been interpreted by some planetary geologists as a rift valleys.[10][11] Some natural satellites also have prominent rift valleys. The 2,000 km long Ithaca Chasma on Tethys in the Saturn system is a prominent example. Charon's Nostromo Chasma is the first confirmed in the Pluto system, however large chasms up to 950 km wide observed on the Charon have also been tentatively interpreted by some as giant rifts and similar formations have also been noted on Pluto.[12] A recent study suggests a complex system of ancient lunar rift valleys including Vallis Rheita and Vallis Alpes.[13] The Uranus system also has prominent examples, with large 'chasma' believed to be giant rift valley systems, most notably the 1492 km long Messina Chasma on Titania, 622 km Kachina Chasmata on Ariel, Verona Rupes on Miranda,[14] and Mommur Chasma on Oberon.[15]
References[edit]
Jump up ^ "The Ethiopian Rift Valley". Giacomo Corti-CNR.
Jump up ^ "The World's Greatest Lakes". Archived from the original on 2006-11-27. Retrieved 2007-01-07.
Jump up ^ "Lake Baikal – World Heritage Site". World Heritage. Retrieved 2007-01-13.
Jump up ^ "The Oddities of Lake Baikal". Alaska Science Forum. Retrieved 2007-01-07.
Jump up ^ Siegert, Martin J. (1999). "Antarctica's Lake Vostok". American Scientist. 87 (6): 510. Bibcode:1999AmSci..87..510S. doi:10.1511/1999.6.510. The best explanation is that Lake Vostok may lie in a rift valley, as does Lake Tanganyika in East Africa and Lake Baikal in Russia. The geography of Lake Vostok is indeed consistent with this notion, in that the lake has a crescent shape, just like Tanganyika and Baikal, and the side walls of the lake are relatively steep, at least on one side.
Jump up ^ John Grotzinger .... (2006). Understanding Earth. New York: W. H. Freeman. ISBN 0-7167-7696-0.
Jump up ^ Anderson, Scott; Grimm, Robert E. (1998). "Rift processes at the Valles Marineris, Mars: Constraints from gravity on necking and rate-dependent strength evolution". Journal of Geophysical Research. 103 (E5): 11113. Bibcode:1998JGR...10311113A. doi:10.1029/98JE00740. ISSN 0148-0227.
Jump up ^ Andrews-Hanna, Jeffrey C. (2012). "The formation of Valles Marineris: 3. Trough formation through super-isostasy, stress, sedimentation, and subsidence". Journal of Geophysical Research. 117 (E6). Bibcode:2012JGRE..117.6002A. doi:10.1029/2012JE004059. ISSN 0148-0227.
Jump up ^ Kiefer, W. S.; Swafford, L. C. (2006). "Topographic Analysis Of Devana Chasma, Venus; Implications For Rift System Segmentation And Propagation". Journal of Structural Geology. 28 (12): 2144–2155. Bibcode:2006JSG....28.2144K. doi:10.1016/j.jsg.2005.12.002.
Jump up ^ Senske, D. A.; Schaber, G. G.; Stofan, E. R. (1992). "Regional topographic rises on Venus: Geology of Western Eistla Regio and comparison to Beta Regio and Atla Regio". Journal of Geophysical Research. 97 (E8): 13395. Bibcode:1992JGR....9713395S. doi:10.1029/92JE01167. ISSN 0148-0227.
Jump up ^ Solomon, Sean C.; Smrekar, Suzanne E.; Bindschadler, Duane L.; Grimm, Robert E.; Kaula, William M.; McGill, George E.; Phillips, Roger J.; Saunders, R. Stephen; Schubert, Gerald; Squyres, Steven W.; Stofan, Ellen R. (1992). "Venus tectonics: An overview of Magellan observations". Journal of Geophysical Research. 97 (E8): 13199. Bibcode:1992JGR....9713199S. doi:10.1029/92JE01418. ISSN 0148-0227.
Jump up ^ Dunn, Marcia (16 July 2015). "'Blowing my mind': Peaks on Pluto, canyons on Charon". PhysOrg.
Jump up ^ Andrews-Hanna, Jeffrey C.; Besserer, Jonathan; Head III, James W.; Howett, Carly J. A.; Kiefer, Walter S.; Lucey, Paul J.; McGovern, Patrick J.; Melosh, H. Jay; Neumann, Gregory A.; Phillips, Roger J.; Schenk, Paul M.; Smith, David E.; Solomon, Sean C.; Zuber, Maria T. (2014). "Structure and evolution of the lunar Procellarum region as revealed by GRAIL gravity data". Nature. 514 (7520): 68–71. Bibcode:2014Natur.514...68A. doi:10.1038/nature13697. ISSN 0028-0836. PMID 25279919.
Jump up ^ Chaikin, Andrew (2001-10-16). "Birth of Uranus' provocative moon still puzzles scientists". space.com. Imaginova Corp. p. 1. Archived from the original on July 9, 2008. Retrieved 2007-07-23.
Jump up ^ Smith, B. A.; Soderblom, L. A.; Beebe, A.; Bliss, D.; Boyce, J. M.; Brahic, A.; Briggs, G. A.; Brown, R. H.; Collins, S. A. (4 July 1986). "Voyager 2 in the Uranian System: Imaging Science Results". Science. 233 (4759): 43–64. Bibcode:1986Sci...233...43S. doi:10.1126/science.233.4759.43. PMID 17812889.
Further reading[edit]
Bonatti, E (1985). "Punctiform initiation of seafloor spreading in the Red Sea during transition from a continental to an oceanic rift". Nature. 316: 33–37. Bibcode:1985Natur.316...33B. doi:10.1038/316033a0.
Mart, Y.; Dauteuil, O. (2000). "Analogue experiments of propagation of oblique rifts". Tectonophysics. 316: 121–132. Bibcode:2000Tectp.316..121M. doi:10.1016/s0040-1951(99)00231-0.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Rift_valley&oldid=850285501"
Categories:
Rifts and grabens
Tectonic landforms
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
العربية
Azərbaycanca
Eesti
Euskara
فارسی
Gaeilge
हिन्दी
Italiano
עברית
Kiswahili
Bahasa Melayu
Nederlands
Norsk
Polski
Slovenščina
Svenska
ไทย
Українська
Vèneto
Tiếng Việt
11 more
Edit links
This page was last edited on 14 July 2018, at 23:13 (UTC).
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

key: html

type: local

value: div

attrs: id class

values: mw-page-base noprint

values: mw-head-base noprint

value: a

attrs: id class lang

values: firstHeading firstHeading en

values: siteSub noprint

attrs: class href

values: mw-jump-link #mw-head

values: mw-jump-link #p-search

attrs: href title

attrs: role class

values:
note
hatnote navigation-not-searchable

attrs: href class title

values:
/wiki/Rift_valley_(disambiguation)
mw-disambig
Rift valley (disambiguation)

value: img

attrs: alt src width height class srcset data-file-width data-file-height

attrs: href class

values:
/wiki/African_Rift_Valley
mw-redirect
African Rift Valley

values: checkbox button toctogglecheckbox toctogglecheckbox display:none

values:
/wiki/Sea_floor_spreading
mw-redirect
Sea floor spreading

values:
/wiki/Tectonic_plate
mw-redirect
Tectonic plate

values:
/wiki/World_Heritage_Site
mw-redirect
World Heritage Site

values:
/wiki/Midcontinent_Rift
mw-redirect
Midcontinent Rift

values: Edit section: Extraterrestrial rift valleys

values:
/wiki/Messina_Chasma
mw-redirect
Messina Chasma

values:
nofollow
external text
http://ethiopianrift.igg.cnr.it

values:
nofollow
external text
http://whc.unesco.org/en/list/754

values:
nofollow
external text
//doi.org/10.1511/1999.6.510

values:
nofollow
external text
//doi.org/10.1029/98JE00740

values:
nofollow
external text
//www.worldcat.org/issn/0148-0227

values:
nofollow
external text
//doi.org/10.1029/2012JE004059

values:
nofollow
external text
//doi.org/10.1016/j.jsg.2005.12.002

values:
nofollow
external text
//doi.org/10.1029/92JE01167

values:
nofollow
external text
//doi.org/10.1029/92JE01418

values:
nofollow
external text
//doi.org/10.1038/nature13697

values:
nofollow
external text
//www.worldcat.org/issn/0028-0836

values:
/wiki/PubMed_Identifier
mw-redirect
PubMed Identifier

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/25279919

values:
nofollow
external text
//doi.org/10.1126/science.233.4759.43

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/17812889

values:
nofollow
external text
//doi.org/10.1038/316033a0

values:
catlinks mw-normal-catlinks
catlinks mw-normal-catlinks
interface

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Rift_valley
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: واد متصدع – Arabic

values:
https://az.wikipedia.org/wiki/Tafrogen
Tafrogen – Azerbaijani
az
az
interlanguage-link-target

values:
interlanguage-link interwiki-az
display: none;

values:
https://et.wikipedia.org/wiki/Riftiorg
Riftiorg – Estonian
et
et
interlanguage-link-target

values:
interlanguage-link interwiki-et
display: none;

values:
interlanguage-link interwiki-eu
display: none;

values: دره کافتی – Persian

values:
interlanguage-link interwiki-ga
display: none;

values: रिफ़्ट घाटी – Hindi

values: עמק ביקוע – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values:
interlanguage-link interwiki-sw
display: none;

values:
https://no.wikipedia.org/wiki/Riftdal
Riftdal – Norwegian
no
no
interlanguage-link-target

values:
interlanguage-link interwiki-no
display: none;

values:
interlanguage-link interwiki-sl
display: none;

values:
https://sv.wikipedia.org/wiki/Sprickdal
Sprickdal – Swedish
sv
sv
interlanguage-link-target

values: หุบเขาทรุด – Thai

values:
interlanguage-link interwiki-th
display: none;

values: Рифтова долина – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values:
interlanguage-link interwiki-vec
display: none;

values: All languages (initial selection from common choices by you and others)

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Rift_valley rootpage-Rift_valley skin-vector action-view


text:
Governor (device)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article is about the concept of self-limiting in mechanics. For other uses, see Self-limiting.
For other uses, see governor (disambiguation).
A governor', or speed limiter' or controller, is a device used to measure and regulate the speed of a machine, such as an engine.
A classic example is the centrifugal governor, also known as the Watt or fly-ball governor on a reciprocating steam engine, which uses the effect of centrifugal force on rotating weights driven by the machine output shaft to regulate its speed by altering the input flow of steam.
Contents
[hide]
1 History
2 Speed limiters
2.1 Cars
2.2 Mopeds
2.3 Public services vehicles
2.4 Trucks (HGVs)
3 Example uses
3.1 Aircraft
3.2 Small engines
3.3 Turbine controls
4 See also
5 References
History[edit]
See also: Control theory
Cut-away drawing of steam engine speed governor. The valve starts fully open at zero speed, and is closed as the balls rotate and rise. The speed sensing drive shaft is top right
Porter governor on a Corliss steam engine
Centrifugal governors were used to regulate the distance and pressure between millstones in windmills since the 17th century. Early steam engines employed a purely reciprocating motion, and were used for pumping water – an application that could tolerate variations in the working speed.
It was not until the Scottish engineer James Watt introduced the rotative steam engine, for driving factory machinery, that a constant operating speed became necessary. Between the years 1775 and 1800, Watt, in partnership with industrialist Matthew Boulton, produced some 500 rotative beam engines. At the heart of these engines was Watt’s self-designed "conical pendulum" governor: a set of revolving steel balls attached to a vertical spindle by link arms, where the controlling force consists of the weight of the balls.
The theoretical basis for the operation of governors was described by James Clerk Maxwell in 1868 in his seminal paper 'On Governors'.[1]
Building on Watt’s design was American engineer Willard Gibbs who in 1872 theoretically analyzed Watt’s conical pendulum governor from a mathematical energy balance perspective. During his Graduate school years at Yale University, Gibbs observed that the operation of the device in practice was beset with the disadvantages of sluggishness and a tendency to over-correct for the changes in speed it was supposed to control.[2]
Gibbs theorized that, analogous to the equilibrium of the simple Watt governor (which depends on the balancing of two torques: one due to the weight of the "balls" and the other due to their rotation), thermodynamic equilibrium for any work producing thermodynamic system depends on the balance of two entities. The first is the heat energy supplied to the intermediate substance, and the second is the work energy performed by the intermediate substance. In this case, the intermediate substance is steam.
These sorts of theoretical investigations culminated in the 1876 publication of the Gibbs' famous work On the Equilibrium of Heterogeneous Substances and in the construction of the Gibbs’ governor. These formulations are ubiquitous today in the natural sciences in the form of the Gibbs' free energy equation, which is used to determine the equilibrium of chemical reactions; also known as Gibbs equilibrium.[3]
Speed limiters[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2009) (Learn how and when to remove this template message)
Main article: Speed limiter
Governors can be used to limit the top speed for vehicles, and for some classes of vehicle such devices are a legal requirement. They can more generally be used to limit the rotational speed of the internal combustion engine or protect the engine from damage due to excessive rotational speed.
Cars[edit]
Today, BMW, Audi, Volkswagen and Mercedes-Benz limit their production cars to 250 kilometres per hour (155 mph). Certain Quattro GmbH and AMG cars, and the Mercedes/McLaren SLR is an exception. The BMW Rolls-Royces are limited to 240 kilometres per hour (149 mph). Jaguars, although British, also have a limiter, as do the Swedish Saab and Volvo on cars where it is necessary.
German manufacturers initially started the "gentlemen's agreement", electronically limiting their vehicles to a top speed of 250 kilometres per hour (155 mph),[4][5] since such high speeds are more likely on the Autobahn. This was done to reduce the political desire to introduce a legal speed limit.
In European markets, General Motors Europe sometimes choose to discount the agreement, meaning that certain high-powered Opel or Vauxhall cars can exceed the 250 kilometres per hour (155 mph) mark, whereas their Cadillacs do not. Ferrari, Lamborghini, Maserati, Porsche, Aston Martin and Bentley also do not limit their cars, at least not to 250 kilometres per hour (155 mph). The Chrysler 300C SRT8 is limited to 270 km/h. Most Japanese domestic market vehicles are limited to only 180 kilometres per hour (112 mph) or 190 kilometres per hour (118 mph).[6] The top speed is a strong sales argument, though speeds above about 300 kilometres per hour (190 mph) are not likely reachable on public roads.[citation needed]
Many performance cars are limited to a speed of 250 kilometres per hour (155 mph)[7] to limit insurance costs of the vehicle, and reduce the risk of tires failing.[citation needed]
Mopeds[edit]
Mopeds in the United Kingdom have had to have a 30 mph (48 km/h) speed limiter since 1977.[8] Most other European countries have similar rules (see the main article).
Public services vehicles[edit]
Public service vehicles often have a legislated top speed. Scheduled coach services in the United kingdom (and also bus services) are limited to 65 mph.[9]
Urban public buses often have speed governors which are typically set to between 65 kilometres per hour (40 mph) and 100 kilometres per hour (62 mph).[citation needed]
Trucks (HGVs)[edit]
All heavy vehicles in Europe and New Zealand have law/by-law governors that limits their speeds to 90 kilometres per hour (56 mph) or 100 kilometres per hour (62 mph).[citation needed] Fire engines and other emergency vehicles are exempt from this requirement.
Example uses[edit]
Aircraft[edit]
Aircraft propellers are another application. The governor senses shaft RPM, and adjusts or controls the angle of the blades to vary the torque load on the engine. Thus as the aircraft speeds up (as in a dive) or slows (in climb) the RPM is held constant.
Small engines[edit]
Small engines, used to power lawn mowers, portable generators, and lawn and garden tractors, are equipped with a governor to limit fuel to the engine to a maximum safe speed when unloaded and to maintain a relatively constant speed despite changes in loading. In the case of generator applications, the engine speed must be closely controlled so the output frequency of the generator will remain reasonably constant.
Small engine governors are typically one of three types:
Pneumatic: the governor mechanism detects air flow from the flywheel blower used to cool an air-cooled engine. The typical design includes an air vane mounted inside the engine's blower housing and linked to the carburetor's throttle shaft. A spring pulls the throttle open and, as the engine gains speed, increased air flow from the blower forces the vane back against the spring, partially closing the throttle. Eventually a point of equilibrium will be reached and the engine will run at a relatively constant speed. Pneumatic governors are simple in design and inexpensive to produce. However, they do not regulate engine speed very accurately and are affected by air density, as well as external conditions that may influence airflow.
Centrifugal: a flyweight mechanism driven by the engine is linked to the throttle and works against a spring in a fashion similar to that of the pneumatic governor, resulting in essentially identical operation. A centrifugal governor is more complex to design and produce than a pneumatic governor. However, the centrifugal design is more sensitive to speed changes and hence is better suited to engines that experience large fluctuations in loading.
Electronic: a servo motor is linked to the throttle and controlled by an electronic module that senses engine speed by counting electrical pulses emitted by the ignition system or a magnetic pickup. The frequency of these pulses varies directly with engine speed, allowing the control module to apply a proportional voltage to the servo to regulate engine speed. Due to their sensitivity and rapid response to speed changes, electronic governors are often fitted to engine-driven generators designed to power computer hardware, as the generator's output frequency must be held within narrow limits to avoid malfunction.
Turbine controls[edit]
Play media
Operation of a flyball governor to control speeds of a water turbine
In steam turbines, the steam turbine governing is the procedure of monitoring and controlling the flow rate of steam into the turbine with the objective of maintaining its speed of rotation as constant. The flow rate of steam is monitored and controlled by interposing valves between the boiler and the turbine.[10]
In water turbines, governors have been used since the mid-19th century to control their speed. A typical system would use a Flyball governor acting directly on the turbine input valve or the wicket gate to control the amount of water entering the turbine. By 1930, mechanical governors started to use PID controllers for more precise control. In the later part of the twentieth century, electronic governors and digital systems started to replace mechanical governors.[11]
See also[edit]
Regulator
Servomechanism
Hit and miss engine
Centrifugal governor
References[edit]
Jump up ^ Bennett, Stuart (1992). A history of control engineering, 1930-1955. IET. p. p. 48. ISBN 978-0-86341-299-8.
Jump up ^ Wheeler, Lynder Phelps (1947), "The Gibbs Governor for Steam Engines", in Wheeler, Lynder Phelps; Waters, Everett Oyler; Dudley, Samuel William, The Early Work of Willard Gibbs in Applied Mechanics, New York: Henry Schuman, pp. 63–78
Jump up ^ Wheeler, L. (1951). Josiah Willard Gibbs - the History of a Great Mind. Woodbridge, CT: Ox Bow Press.
Jump up ^ Bogdan Popa. "Gentlemen’s Agreement: Not So Fast, Sir!". autoevolution.
Jump up ^ van Gorp, Anke. "Ethical Issues in Engineering Design; Safety and Sustainability" page 16. Published by 3TU Ethics, 2005. ISBN 9090199071, 9789090199078 . ISSN 1574-941X
Jump up ^ "Why Japan finally got its foot off the brake | The Japan Times Online". Search.japantimes.co.jp. 2008-04-13. Retrieved 2012-11-08.
Jump up ^ Mike Spinelli. "So Long Guv'nor: Mercedes Will Unlock Top Speed on AMG Models in the US, for a Price". Jalopnik.
Jump up ^ Department for Transport (2008). "Reported Road Casualties Great Britain: 2008 Annual Report" (PDF). Retrieved 2010-01-09. p.179 states: "Mopeds redefined to 30 mph maximum design speed"
Jump up ^ "History of British road safety". Retrieved 2010-01-20.
Jump up ^ Rathore, M.M. (2010). Thermal engineering. New Delhi: Tata McGraw-Hill Education. ISBN 978-0-07-068113-2. Retrieved 29 January 2015.
Jump up ^ Fasol, Karl Heinz (August 2002). "A Short History of Hydropower Control" (PDF). IEEE Control Systems Magazine: 68–76. Retrieved 29 January 2015.
Wikimedia Commons has media related to Governor (device).
Retrieved from "https://en.wikipedia.org/w/index.php?title=Governor_(device)&oldid=805331120"
Categories:
Mechanisms (engineering)
Mechanical power control
Hidden categories:
Articles needing additional references from November 2009
All articles needing additional references
All articles with unsourced statements
Articles with unsourced statements from November 2009
Articles with unsourced statements from May 2012
Commons category with page title different than on Wikidata
Articles containing video clips
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
فارسی
한국어
Latina
Nederlands
日本語
Svenska
தமிழ்
Edit links
This page was last edited on 14 October 2017, at 17:26.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

values:
/wiki/Self-limiting_(disambiguation)
mw-redirect mw-disambig
Self-limiting (disambiguation)

values:
note
hatnote navigation-not-searchable

values:
/wiki/Governor_(disambiguation)
mw-disambig
Governor (disambiguation)

value: i

value: p

values:
/wiki/Willard_Gibbs
mw-redirect
Willard Gibbs

attrs: alt src width height srcset data-file-width data-file-height

values: Help:Introduction to referencing with Wiki Markup/1

values: plainlinks metadata ambox ambox-content ambox-Refimprove

values:
/wiki/Quattro_GmbH
mw-redirect
Quattro GmbH

values: This claim needs references to reliable sources. (November 2009)

values:
noprint Inline-Template Template-Fact
white-space:nowrap;

values: This claim needs references to reliable sources. (May 2012)

values:
/wiki/Heavy_vehicle
mw-redirect
Heavy vehicle

values:
/wiki/Propeller_(aircraft)
mw-redirect
Propeller (aircraft)

values:
/wiki/Fan_(mechanical)
mw-redirect
Fan (mechanical)

values:
/wiki/Servo_motor
mw-redirect
Servo motor

values: <video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/From_Turbine_to_Line_Shaft.webm/854px--From_Turbine_to_Line_Shaft.webm.jpg" controls="" preload="none" autoplay="" style="width:854px;height:480px" class="kskin" data-durationhint="113.683" data-startoffset="0" data-mwtitle="From_Turbine_to_Line_Shaft.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/From_Turbine_to_Line_Shaft.webm/From_Turbine_to_Line_Shaft.webm.480p.webm" type="video/webm; codecs="vp8, vorbis"" data-title="SD WebM (480P)" data-shorttitle="WebM 480P" data-transcodekey="480p.webm" data-width="854" data-height="480" data-bandwidth="1073504" data-framerate="29.97"/><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/From_Turbine_to_Line_Shaft.webm/From_Turbine_to_Line_Shaft.webm.720p.webm" type="video/webm; codecs="vp8, vorbis"" data-title="HD WebM (720P)" data-shorttitle="WebM 720P" data-transcodekey="720p.webm" data-width="1280" data-height="720" data-bandwidth="1633968" data-framerate="29.97"/><source src="//upload.wikimedia.org/wikipedia/commons/5/55/From_Turbine_to_Line_Shaft.webm" type="video/webm; codecs="vp8, vorbis"" data-title="Original WebM file, 1,920 × 1,080 (2.24 Mbps)" data-shorttitle="WebM source" data-width="1920" data-height="1080" data-bandwidth="2244641" data-framerate="29.97"/><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/From_Turbine_to_Line_Shaft.webm/From_Turbine_to_Line_Shaft.webm.1080p.webm" type="video/webm; codecs="vp8, vorbis"" data-title="Full HD WebM (1080P)" data-shorttitle="WebM 1080P" data-transcodekey="1080p.webm" data-width="1920" data-height="1080" data-bandwidth="2416760" data-framerate="29.97"/><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/From_Turbine_to_Line_Shaft.webm/From_Turbine_to_Line_Shaft.webm.160p.webm" type="video/webm; codecs="vp8, vorbis"" data-title="Low bandwidth WebM (160P)" data-shorttitle="WebM 160P" data-transcodekey="160p.webm" data-width="284" data-height="160" data-bandwidth="198152" data-framerate="29.97"/><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/From_Turbine_to_Line_Shaft.webm/From_Turbine_to_Line_Shaft.webm.240p.webm" type="video/webm; codecs="vp8, vorbis"" data-title="Small WebM (240P)" data-shorttitle="WebM 240P" data-transcodekey="240p.webm" data-width="426" data-height="240" data-bandwidth="316888" data-framerate="29.97"/><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/From_Turbine_to_Line_Shaft.webm/From_Turbine_to_Line_Shaft.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-title="WebM (360P)" data-shorttitle="WebM 360P" data-transcodekey="360p.webm" data-width="640" data-height="360" data-bandwidth="567544" data-framerate="29.97"/></video>

values:
/wiki/Hit_and_miss_engine
mw-redirect
Hit and miss engine

values: Category:Articles needing additional references from November 2009

values: Category:All articles needing additional references

values: Category:All articles with unsourced statements

values: Category:Articles with unsourced statements from November 2009

values: Category:Articles with unsourced statements from May 2012

values: Category:Commons category with page title different than on Wikidata

values: Category:Articles containing video clips

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Governor_(device)
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values:
uls-settings-trigger
Language settings
0
button
true

values: گاورنر – Persian

values: கட்டுப்படுத்தி – Tamil

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Governor_device rootpage-Governor_device vector-experimental-print-styles vector-nav-directionality skin-vector action-view