Skewness, the Glossary
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.[1]
Table of Contents
63 relations: Absolute value, Average absolute deviation, Bias of an estimator, Biometrika, Bragg peak, C. R. Rao, Central moment, Confidence interval, Consistent estimator, Cornish–Fisher expansion, Coskewness, Cumulant, Cumulative distribution function, D'Agostino's K-squared test, Expected value, Goodness of fit, Heavy-tailed distribution, Histogram, Infimum and supremum, Interquartile range, Journal of the Royal Statistical Society, Karl Pearson, Kurtosis, L-moment, Log-normal distribution, Long tail, Mean, Medcouple, Median, Method of moments (statistics), Microsoft Excel, Minitab, Mode (statistics), Moment (mathematics), Multimodal distribution, Nonparametric skew, Normal distribution, Normality test, OpenStax, Outlier, Probability distribution, Probability theory, Q–Q plot, Quantile function, Random variable, Real number, Robust statistics, Ronald Fisher, Sample mean and covariance, Sampling (statistics), ... Expand index (13 more) »
- Moment (mathematics)
Absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign.
See Skewness and Absolute value
Average absolute deviation
The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. Skewness and average absolute deviation are statistical deviation and dispersion.
See Skewness and Average absolute deviation
Bias of an estimator
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated.
See Skewness and Bias of an estimator
Biometrika
Biometrika is a peer-reviewed scientific journal published by Oxford University Press for the.
Bragg peak
The Bragg peak is a pronounced peak on the Bragg curve which plots the energy loss of ionizing radiation during its travel through matter.
C. R. Rao
Calyampudi Radhakrishna Rao (10 September 1920 – 22 August 2023) was an Indian-American mathematician and statistician.
Central moment
In probability theory and statistics, a central moment is a moment of a probability distribution of a random variable about the random variable's mean; that is, it is the expected value of a specified integer power of the deviation of the random variable from the mean. Skewness and central moment are moment (mathematics) and statistical deviation and dispersion.
See Skewness and Central moment
Confidence interval
Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated.
See Skewness and Confidence interval
Consistent estimator
In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter θ0—having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to θ0.
See Skewness and Consistent estimator
Cornish–Fisher expansion
The Cornish–Fisher expansion is an asymptotic expansion used to approximate the quantiles of a probability distribution based on its cumulants. Skewness and Cornish–Fisher expansion are statistical deviation and dispersion.
See Skewness and Cornish–Fisher expansion
Coskewness
In probability theory and statistics, coskewness is a measure of how much three random variables change together.
Cumulant
In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Skewness and cumulant are moment (mathematics).
Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow satisfying \lim_F(x).
See Skewness and Cumulative distribution function
D'Agostino's K-squared test
In statistics, D'Agostino's K2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to gauge the compatibility of given data with the null hypothesis that the data is a realization of independent, identically distributed Gaussian random variables.
See Skewness and D'Agostino's K-squared test
Expected value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
See Skewness and Expected value
Goodness of fit
The goodness of fit of a statistical model describes how well it fits a set of observations.
See Skewness and Goodness of fit
Heavy-tailed distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution.
See Skewness and Heavy-tailed distribution
Histogram
A histogram is a visual representation of the distribution of quantitative data.
Infimum and supremum
In mathematics, the infimum (abbreviated inf;: infima) of a subset S of a partially ordered set P is the greatest element in P that is less than or equal to each element of S, if such an element exists.
See Skewness and Infimum and supremum
Interquartile range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data.
See Skewness and Interquartile range
Journal of the Royal Statistical Society
The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.
See Skewness and Journal of the Royal Statistical Society
Karl Pearson
Karl Pearson (born Carl Pearson; 27 March 1857 – 27 April 1936) was an English eugenicist, mathematician, and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university statistics department at University College London in 1911, and contributed significantly to the field of biometrics and meteorology.
Kurtosis
In probability theory and statistics, kurtosis (from κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. Skewness and kurtosis are moment (mathematics) and statistical deviation and dispersion.
L-moment
In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution. Skewness and l-moment are moment (mathematics).
Log-normal distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.
See Skewness and Log-normal distribution
Long tail
In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having many occurrences far from the "head" or central part of the distribution.
Mean
A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers. Skewness and mean are moment (mathematics).
Medcouple
In statistics, the medcouple is a robust statistic that measures the skewness of a univariate distribution. Skewness and medcouple are statistical deviation and dispersion.
The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.
Method of moments (statistics)
In statistics, the method of moments is a method of estimation of population parameters. Skewness and method of moments (statistics) are moment (mathematics).
See Skewness and Method of moments (statistics)
Microsoft Excel
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.
See Skewness and Microsoft Excel
Minitab
Minitab is a statistics package developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in conjunction with Triola Statistics Company in 1972.
Mode (statistics)
In statistics, the mode is the value that appears most often in a set of data values.
See Skewness and Mode (statistics)
Moment (mathematics)
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.
See Skewness and Moment (mathematics)
Multimodal distribution
In statistics, a multimodal distribution is a probability distribution with more than one mode (i.e., more than one local peak of the distribution).
See Skewness and Multimodal distribution
Nonparametric skew
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.
See Skewness and Nonparametric skew
Normal distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.
See Skewness and Normal distribution
Normality test
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
See Skewness and Normality test
OpenStax
OpenStax (formerly OpenStax College) is a nonprofit educational technology initiative based at Rice University.
Outlier
In statistics, an outlier is a data point that differs significantly from other observations.
Probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.
See Skewness and Probability distribution
Probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability.
See Skewness and Probability theory
Q–Q plot
In statistics, a Q–Q plot (quantile–quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other.
Quantile function
In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value.
See Skewness and Quantile function
Random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.
See Skewness and Random variable
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
Robust statistics
Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect.
See Skewness and Robust statistics
Ronald Fisher
Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic.
See Skewness and Ronald Fisher
Sample mean and covariance
The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables.
See Skewness and Sample mean and covariance
Sampling (statistics)
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population.
See Skewness and Sampling (statistics)
SAS (software)
SAS (previously "Statistical Analysis System") is a statistical software suite developed by SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, criminal investigation, and predictive analytics.
See Skewness and SAS (software)
Shape parameter
In probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributions that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).
See Skewness and Shape parameter
Skew normal distribution
In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.
See Skewness and Skew normal distribution
Skewness risk
Skewness risk in financial modeling is the risk that results when observations are not spread symmetrically around an average value, but instead have a skewed distribution. Skewness and Skewness risk are statistical deviation and dispersion.
See Skewness and Skewness risk
SPSS
SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation.
Standard deviation
In statistics, the standard deviation is a measure of the amount of variation of a random variable expected about its mean. Skewness and standard deviation are statistical deviation and dispersion.
See Skewness and Standard deviation
Standardized moment
In probability theory and statistics, a standardized moment of a probability distribution is a moment (often a higher degree central moment) that is normalized, typically by a power of the standard deviation, rendering the moment scale invariant. Skewness and standardized moment are moment (mathematics) and statistical deviation and dispersion.
See Skewness and Standardized moment
Statistical dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Skewness and Statistical dispersion are statistical deviation and dispersion.
See Skewness and Statistical dispersion
Statistical hypothesis test
A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently support a particular hypothesis.
See Skewness and Statistical hypothesis test
Statistics
Statistics (from German: Statistik, "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Symmetric probability distribution
In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some value of the random variable represented by the distribution.
See Skewness and Symmetric probability distribution
Unimodality
In mathematics, unimodality means possessing a unique mode.
Value at risk
Value at risk (VaR) is a measure of the risk of loss of investment/Capital.
See Skewness and Value at risk
See also
Moment (mathematics)
- Carleman's condition
- Central moment
- Cumulant
- Factorial moment
- Factorial moment generating function
- Generalized method of moments
- Hamburger moment problem
- Hausdorff moment problem
- Isserlis' theorem
- Kurtosis
- L-moment
- Mean
- Method of moments (probability theory)
- Method of moments (statistics)
- Moment (mathematics)
- Moment measure
- Moment problem
- Moment-generating function
- Optimal instruments
- Second moment method
- Skewness
- Standardized moment
- Stieltjes moment problem
- Taylor expansions for the moments of functions of random variables
- Variance
References
[1] https://en.wikipedia.org/wiki/Skewness
Also known as Left-tailed distribution, Negative skew, Negative skewness, Pearson's skewness coefficients, Positive skew, Positive skewness, Positively skewed, Right-skewed, Right-skewed curve, Right-skewed distribution, Right-tailed distribution, Sample skewness, Skew distribution, Skewed, Skewed data, Skewed distribution, Skewed left, Skewed right, Skewedness, Skewity, Unbalanced data, Y-K index, Yule–Kendall index.
, SAS (software), Shape parameter, Skew normal distribution, Skewness risk, SPSS, Standard deviation, Standardized moment, Statistical dispersion, Statistical hypothesis test, Statistics, Symmetric probability distribution, Unimodality, Value at risk.