2017/10/26 by Dimitris Askitis, Askitis, Dimitris
Computer Science · Mathematics · #26A51 #33B20 #60E05 #Bayesian Methods and Mixture Models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #math.CA #msc:26A51 #msc:33B20 #msc:60E05
paper · pdf · doi:10.48550/arxiv.1710.09708
17 pages, 3 figures
arxiv created 2017/10/26 · openalex publication_date 2017/10/26 · arxiv updated 2017/10/27 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
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 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.