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.

中文翻译：

---

广义正态分布族的 Fisher 信息

在这个简短的笔记中，我们计算了广义正态分布族的 Fisher 信息。Fisher 信息通常是为正则分布定义的，即连续可微（对数）密度函数，其支持度不依赖于族参数 $\theta$。尽管 $[-\theta, + \theta]$ 中的均匀分布不满足正则性要求，但作为我们结果的一个特例，我们将获得该族的 Fisher 信息。