A Cautionary Note on Beta Families of Distributions and the Aliases Within. Issue 2 (3rd April 2018)

• Record Type: Journal Article
• Authors: Hutson, Alan D.; Vexler, Albert
• Is Part Of: American statistician. Volume 72:Issue 2(2018)
• Page Start: 121
• Page End: 129
• Publication Date: 2018-04-03
• Subjects: Maximum likelihood estimation -- Numerical methods -- Parametric models; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2016.1213661
• Languages: English
• ISSNs: 0003-1305

Abstract

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.