The Weibull – Burr XII {log logistic} Poisson lifetime model

Abstract

A new flexible probability distribution which extends the classical Burr XII distribution for fitting unimodal datasets with various shape and tail behaviors is introduced in this paper. The distribution is so-called the Weibull – Burr XII {log logistic} Poisson distribution and was realized by compounding the Weibull – Burr XII {log logistic} distribution from the T – R {Y} family of probability distributions and the Poisson distribution and hence, the distribution belongs to the T – R {Y} Poisson class. A detailed account of the statistical properties of the distribution including moments, quantiles, mode and mean deviations are presented. The maximum likelihood estimation method is suggested for the estimation of the parameters of the distribution and Monte Carlo simulations study is used to assess its performance. Three data sets with various shape and tail properties are further used to test the applicability of the new distribution.