Convex transform order of Beta distributions with some consequences

Idir Arab, Paulo Eduardo Oliveira and Tilo Wiklund

Statistica Neerlandica, 2021, vol. 75, issue 3, 238-256

Abstract: The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterization of when one Beta distribution is smaller than another according to the convex transform order. As an application, we derive monotonicity properties for the probability of Beta distributed random variables exceeding the mean or mode of their distribution. Moreover, we obtain a simple alternative proof of the mode‐median‐mean inequality for unimodal distributions that are skewed in a sense made precise by the convex transform order. This new proof also gives an analogous inequality for the anti‐mode of distributions that have a unique anti‐mode. Such inequalities for Beta distributions follow as special cases. Finally, some consequences for the values of distribution functions of binomial distributions near to their means are mentioned.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1111/stan.12233

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:stanee:v:75:y:2021:i:3:p:238-256

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0039-0402

Access Statistics for this article

Statistica Neerlandica is currently edited by Miroslav Ristic, Marijtje van Duijn and Nan van Geloven

More articles in Statistica Neerlandica from Netherlands Society for Statistics and Operations Research
Bibliographic data for series maintained by Wiley Content Delivery ().