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Math Help - Types of Gaussian Distributions.

  1. #1
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    Types of Gaussian Distributions.

    Hi all.
    It is known that Gaussian distribution is a case of Normal Distribution (which follows the laws of nature). I wish to know what does a data represent if follows a Super Gaussian distribution? It has a graph flattened around a mean (positive kurtosis). Is it still a type of Normal Distribution?
    Thanks.
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    Quote Originally Posted by beezee99 View Post
    Hi all.
    It is known that Gaussian distribution is a case of Normal Distribution (which follows the laws of nature). I wish to know what does a data represent if follows a Super Gaussian distribution? It has a graph flattened around a mean (positive kurtosis). Is it still a type of Normal Distribution?
    Thanks.
    From Wikipedia:

    A distribution with positive excess kurtosis is called leptokurtic, or leptokurtotic. "Lepto-" means "slender"[1]. In terms of shape, a leptokurtic distribution has a more acute peak around the mean (that is, a higher probability than a normally distributed variable of values near the mean) and fatter tails (that is, a higher probability than a normally distributed variable of extreme values). Examples of leptokurtic distributions include the Laplace distribution and the logistic distribution. Such distributions are sometimes termed super Gaussian.
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    Is it still a type of Normal Distribution?
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  4. #4
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    No. The Normal Distribution necessarily has excess kurtosis equal to 0.

    The Laplace distribution is Super Gaussian but obviously not normal.
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