Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am wondering whether a family of probability distributions with the following form of a density function has a name:


where $A$, $B$ and $C$ are positive constants, with $B$ being a "scaling" constant and $C$ selected so that $f(x)$ integrates to 1.

When $A=1$ this corresponds to a Laplace distribution (with $B=1/b$ and $C=1/2b$ to obtain variance is $2b^2$) and $A=2$ yields the Gaussian distribution (for variance $\sigma^2$ we set $B=1/2\sigma^2$ and $C=1/\sqrt{2\pi\sigma^2}$).

I realize that this belongs to the exponential family. I am just wondering if this specific form has been studied and whether it has any interesting properties (in addition to the properties of the exponential family)... If there is a good reference discussing this, please post.

share|cite|improve this question
Generalized normal distribution – S.B. Sep 13 '12 at 20:02
Thank you, @sbahmani! If you submit your one-liner as an answer, I'll accept it. – M.B.M. Sep 13 '12 at 20:11
up vote 3 down vote accepted

Generalized normal distribution!

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.