# Math Help - Types of Gaussian Distributions.

1. ## 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.

2. Originally Posted by beezee99
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.

3. Is it still a type of Normal Distribution?

4. No. The Normal Distribution necessarily has excess kurtosis equal to 0.

The Laplace distribution is Super Gaussian but obviously not normal.