Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter

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The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as a univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.

Original languageEnglish
JournalMathematica Scandinavica
Volume127
Issue number1
Pages (from-to)111-130
ISSN0025-5521
DOIs
Publication statusPublished - 2021

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