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 (with mean and variance ) and it includes the Laplace distribution when . As, the density converges pointwise to a uniform density on .
This family allows for tails that are either heavier than normal (when ) or lighter than normal (when ). It is a useful way to parametrize a continuum of symmetric, platykurtic densities spanning from the normal to the uniform density, and a continuum of symmetric, leptokurtic densities spanning from the Laplace to the normal density .
Read more about this topic: Generalized Normal Distribution
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