Year: 2024
Type: article
Abstract: Write pbeta(·,α,β) for the distribution function of the Beta distribution with parameters α and β. We show that α↦pbeta(α/(α+β),α,β) is decreasing and α↦pbeta(α/(α+β),α+1,β) is increasing over the positive reals, with the common limit for α→∞ expressible in terms of the Gamma distribution functions, and discuss implications for the distribution functions of the Gamma, Poisson and Binomial distributions.
Source: Entropy
DOI: 10.3390/e26110938
Author: Kurt Hornik
Institution: Vienna University of Economics and Business
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4403977040