On the problem of the unique characterization of discrete distributions by single regression of weak records. Issue 3 (4th May 2018)

• Record Type: Journal Article
• Authors: Bieniek, Mariusz; Maciąg, Krystyna
• Is Part Of: Statistics. Volume 52:Issue 3(2018)
• Page Start: 533
• Page End: 551
• Publication Date: 2018-05-04
• Subjects: Characterization -- regression -- discrete records -- weak records; 62G30 -- 62E10 -- 60E05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1469022
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We consider the problem of the unique identification of discrete probability distributions by the single regression function of non-adjacent discrete weak record values. We present a new approach to this problem and we show that the uniqueness of the characterization is equivalent to the uniqueness of solution to a corresponding difference equation or an appropriate system of difference equations. This result is applied to obtain known as well as new characterizations of discrete distributions.