ABSTRACT In this note, we examine the four parameter beta family of distributions in the context of the beta-normal and beta-logistic distributions. In the process, we highlight the concept of numerical and limiting alias distributions, which in turn relate to numerical instabilities in the numerical maximum likelihood fitting routines for these families of distributions. We conjecture that the numerical issues pertaining to fitting these multiparameter distributions may be more widespread than has originally been reported across several families of distributions.

中文翻译：

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关于分布的 Beta 系列及其内部别名的注意事项

摘要 在本说明中，我们在 beta 正态分布和 beta 逻辑分布的上下文中检查了四参数 beta 分布族。在这个过程中，我们强调了数值和限制别名分布的概念，这反过来又与这些分布族的数值最大似然拟合例程中的数值不稳定性有关。我们推测与拟合这些多参数分布有关的数值问题可能比最初在几个分布系列中报告的问题更为普遍。