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Generalized normal distribution : ウィキペディア英語版
Generalized normal distribution
The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "version 1" and "version 2". However this is not a standard nomenclature.
==Version 1==

Known also as the exponential power distribution, or the generalized error distribution, this is a parametric family of symmetric distributions. It includes all normal and Laplace distributions, and as limiting cases it includes all continuous uniform distributions on bounded intervals of the real line.
This family includes the normal distribution when \textstyle\beta=2 (with mean \textstyle\mu and variance \textstyle \frac) and it includes the Laplace distribution when \textstyle\beta=1. As \textstyle\beta\rightarrow\infty, the density converges pointwise to a uniform density on \textstyle (\mu-\alpha,\mu+\alpha).
This family allows for tails that are either heavier than normal (when \beta<2) or lighter than normal (when \beta>2). It is a useful way to parametrize a continuum of symmetric, platykurtic densities spanning from the normal (\textstyle\beta=2) to the uniform density (\textstyle\beta=\infty), and a continuum of symmetric, leptokurtic densities spanning from the Laplace (\textstyle\beta=1) to the normal density (\textstyle\beta=2).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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