An one-parameter compounding discrete distribution. Issue 8 (11th June 2022)

• Record Type: Journal Article
• Authors: Altun, Emrah; Cordeiro, Gauss M.; Ristić, Miroslav M.
• Is Part Of: Journal of applied statistics. Volume 49:Issue 8(2022)
• Page Start: 1935
• Page End: 1956
• Publication Date: 2022-06-11
• Subjects: Discrete distribution -- compounding -- Poisson distribution -- xgamma distribution; 62E15; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2021.1884846
• Languages: English
• ISSNs: 0266-4763

Abstract

ABSTRACT: In this study, a new one-parameter discrete distribution obtained by compounding the Poisson and xgamma distributions is proposed. Some statistical properties of the new distribution are obtained including moments and probability and moment generating functions. Two methods are used for the estimation of the unknown parameter: the maximum likelihood method and the method of moments. Additionally, the count regression model and integer-valued autoregressive process of the proposed distribution are introduced. Some possible applications of the introduced models are considered and discussed.