Fisher Information of a Family of Generalized Normal Distributions

TL;DR

This paper calculates the Fisher information for a family of generalized normal distributions, including the uniform distribution as a special case, expanding understanding of Fisher information beyond regular distributions.

Contribution

It derives the Fisher information for a broad family of distributions, including non-regular cases like the uniform distribution, which is typically excluded.

Findings

Fisher information computed for generalized normal distributions

Includes the uniform distribution as a special case

Extends Fisher information analysis to non-regular distributions

Abstract

In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support does not depend on the family parameter $\theta$. Although the uniform distribution in $[-\theta, + \theta]$ does not satisfy the regularity requirements, as a special case of our result, we will obtain the Fisher information for this family.