This note shows that the matrix forms of several one-parameter distribution families satisfy a hierarchical low-rank structure. Such families of distributions include binomial, Poisson, and $\chi^2$ distributions. The proof is based on a uniform relative bound of a related divergence function. Numerical results are provided to confirm the theoretical findings.

中文翻译：

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参数化分布的分层低秩结构

此注释显示，几个单参数分布族的矩阵形式满足分层的低秩结构。这样的分布族包括二项分布，泊松分布和$ \ chi ^ 2 $分布。该证明基于相关散度函数的统一相对边界。提供数值结果以证实理论发现。