Bedbur Stefan, Kamps Udo
Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany.
Entropy (Basel). 2021 Jun 8;23(6):726. doi: 10.3390/e23060726.
Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback-Leibler divergence, the Cressie-Read divergence, the Rényi divergence, and the Hellinger metric, can be explicitly expressed in terms of the respective cumulant function and mean value function. Moreover, the same applies to related entropy and affinity measures. We compile representations scattered in the literature and present a unified approach to the derivation in exponential families. As a statistical application, we highlight their use in the construction of confidence regions in a multi-sample setup.
在指数族中，其可能由多参数和多变量分布组成，多种散度度量，如库尔贝克 - 莱布勒散度、克雷斯 - 里德散度、雷尼散度和赫林格度量，可以根据各自的累积量函数和均值函数明确表示出来。此外，相关的熵和亲和度度量也是如此。我们汇编了文献中分散的表示形式，并提出了一种在指数族中进行推导的统一方法。作为一个统计应用，我们强调它们在多样本设置中构建置信区域的用途。
