The Discrete Inverse Burr Distribution with Characterizations, Properties, Applications, Bayesian and Non-Bayesian Estimations

Christophe Chesneau; Haitham Yousof; G.G. Hamedani; Mohamed Ibrahim

doi:10.19139/soic-2310-5070-1393

Christophe Chesneau University of Caen, France
Haitham Yousof Benha university, Egypt
G.G. Hamedani Department of Mathematical and Statistical Sciences, Marquette University, USA
Mohamed Ibrahim Damietta University, Damietta, Egypt

DOI: https://doi.org/10.19139/soic-2310-5070-1393

Keywords: discretization, characterization, weighted least square estimation, maximum likelihood estimation, count data, Bayesian estimation, ordinary least square estimation

Abstract

A new one-parameter heavy tailed discrete distribution with infinite mean is defined and studied. The probability mass function of the new distribution can be "unimodal and right skewed" and its failure rate can be monotonically decreasing. Some of its relevant properties are discussed. Some characterizations based on: (i) the conditional expectation of a certain function of the random variable and (ii) in terms of the reversed hazard function are presented. Different Bayesian and non-Bayesian estimation methods are described and compared using simulations and two real data applications are given. The new model is used to model carious teeth data and counts of cysts in kidneys datasets, and it outperforms many well-known competitive discrete models.

Author Biography

Christophe Chesneau, University of Caen, France

LMNO, Mathematics department

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