Am Stat 2018 26;72(2):121-129. Epub 2018 Jan 26.
Alan D. Hutson is Professor of Oncology, Roswell Park Cancer Institute, Department of Biostatistics & Bioinformatics, Elm & Carlton Streets, Buffalo, NY 14623. Albert Vexler is Associate Professor, University at Buffalo, Department of Biostatistics, 706 Kimball Tower, 3435 Main St., Buffalo, NY 14214-3000.
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. Read More