A Cautionary Note on Beta Families of Distributions and the Aliases Within

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.