Open AccessThe Discrete Inverse Burr Distribution with Characterizations, Properties, Applications, Bayesian and Non-Bayesian Estimations
Author(s) -
Christophe Chesneau,
Haitham M. Yousof,
G. G. Hamedani,
Mohamed Ibrahim
Publication year - 2022
Publication title -
statistics, optimization and information computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.297
H-Index - 12
eISSN - 2311-004X
pISSN - 2310-5070
DOI - 10.19139/soic-2310-5070-1393
Subject(s) - mathematics , bayesian probability , monotonic function , statistics , function (biology) , probability mass function , conditional probability distribution , hazard , inverse , random variable , algorithm , mathematical analysis , chemistry , organic chemistry , evolutionary biology , biology , geometry
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.