CONVOLUTION OF BETA PRIME DISTRIBUTION

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Ferreira, RAC (Author) Other; Simon, T (Author) Other

Journal

Title: Transactions of the American Mathematical Society

Vol. 376

Pages: 855-890

ISSN: 0002-9947

Publisher: American Mathematical Society

Indexing

ISI Web of Knowledge - 0 Citations

Scopus

Other information

Authenticus ID: P-00X-NWP

DOI: 10.1090/tran/8748

Abstract (EN): We establish some identities in law for the convolution of a beta prime distribution with itself, involving the square root of beta distributions. The proof of these identities relies on transformations on generalized hypergeometric series obtained via Appell series of the first kind and Thomae's relationships for F-3(2)(1). Using a self-decomposability argument, the identities are applied to derive complete monotonicity properties for quotients of confluent hypergeometric functions having a doubling character. By means of probability, we also obtain a simple proof of Turan's inequality for the parabolic cylinder function and the confluent hypergeometric function of the second kind. The case of Mill's ratio is discussed in detail.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36