Generalized Error Distribution Wikipedia
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improve this article by introducing more precise citations. (September 2015) (Learn how and when to remove this template message) In probability and statistics, the skewed generalized “t” distribution is a family of continuous probability distributions. The distribution was first introduced by Panayiotis Theodossiou[1] generalized gaussian distribution matlab code in 1998. The distribution has since been used in different applications.[2][3][4][5][6][7] There are different parameterizations generalized normal distribution r for the skewed generalized t distribution,[1][5] which we account for in this article. Contents 1 Definition 1.1 Probability density function 1.2 Moments 2
Skewed Generalized Error Distribution
Special Cases 2.1 skewed generalized error distribution 2.2 generalized t distribution 2.3 skewed t distribution 2.4 skewed Laplace distribution 2.5 generalized error distribution 2.6 skewed normal distribution 2.7 student's t-distribution 2.8 skewed Cauchy distribution 2.9 Laplace distribution
Error Distribution Definition
2.10 Uniform Distribution 2.11 Normal distribution 2.12 Cauchy Distribution 3 References 4 External links 5 Notes Definition[edit] Probability density function[edit] f S G T ( x ; μ , σ , λ , p , q ) = p 2 v σ q 1 / p B ( 1 p , q ) ( | x − μ + m | p q ( v σ ) p ( λ s i g n ( x parametric generalized gaussian density estimation − μ + m ) + 1 ) p + 1 ) 1 p + q {\displaystyle f_ σ 7(x;\mu ,\sigma ,\lambda ,p,q)={\frac σ 6 σ 5B({\frac σ 4 σ 3},q)({\frac {|x-\mu +m|^ σ 2} σ 1(\lambda sign(x-\mu +m)+1)^ σ 0}}+1)^{{\frac π 9 π 8}+q}}}} where B {\displaystyle B} is the beta function, μ {\displaystyle \mu } is the location parameter, σ > 0 {\displaystyle \sigma >0} is the scale parameter, − 1 < λ < 1 {\displaystyle -1<\lambda <1} is the skewness parameter, and p > 0 {\displaystyle p>0} and q > 0 {\displaystyle q>0} are the parameters that control the kurtosis. Note that m {\displaystyle m} and v {\displaystyle v} are not parameters, but functions of the other parameters that are used here to scale or shift the distribution appropriately to match the various parameterizations of this distribution. In the original parameterization[1] of the skewed generalized t distribution, m = 2 v σ λ q 1 p B ( 2 p , q − 1 p ) B ( 1 p , q ) {\displaystyle m={\frac σ 7 σ 6}B({\frac σ 5 σ 4},q-{\frac σ 3 σ 2})} σ 1 σ 0},q)}}} and v = q − 1 p ( 3 λ 2 + 1 ) B ( 3 p , q − 2 p ) B ( 1 p , q ) ȡ
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Generalized Error Distribution R
(GED) in Stata From Stas Kolenikov
Curve) Z-table (Right of Curve) Probability and Statistics Statistics Basics Probability Regression Analysis Critical Values, Z-Tables http://www.statisticshowto.com/generalized-error-distribution-generalized-normal/ & Hypothesis Testing Normal Distributions: Definition, Word Problems T-Distribution Non Normal Distribution Chi Square Design of Experiments Multivariate Analysis Sampling in Statistics Famous Mathematicians and Statisticians Calculators Variance and Standard Deviation Calculator Tdist Calculator Permutation Calculator / Combination Calculator Interquartile Range Calculator Linear Regression Calculator Expected Value Calculator Binomial Distribution error distribution Calculator Statistics Blog Calculus Matrices Practically Cheating Statistics Handbook Navigation Generalized Error Distribution / Generalized Normal Statistics Definitions > Generalized Error Distribution / Generalized Normal What is a Generalized Error Distribution? Generalized error distributions (sometimes called generalized normal distributions) are a symmetric family of distributions used in mathematical modeling, usually when generalized error distribution errors (the difference between the expected value and the observed values) aren't normally distributed. Special cases of this distribution are identical to the normal distribution and the Laplace distribution. The Generalized error distribution is useful when the errors around the mean or in the tails are of special interest. If other deviations from the normal distribution are being studied, other families of distributions can be used. For example, the t-distribution is used if the tails are of interest; the t-distribution approximates the normal distribution as degrees of freedom in the distribution approach infinity. Three parameters define the distribution: The mean, μ, which determines the mode (the peak) of the distribution. Like the standard normal distribution, the median and mode are equal to μ. The standard deviation, σ, which determines the dispersion. A shape parameter, Β. Some authors refer to this as kurtosis, as kurtosis determines how peaked or how flat