The type I half-logistic Burr X distribution: theory and practice

In this paper, we explore the properties and importance of a lifetime distribution so called type I half-logistic Burr X (TIHLBX) in detail (also called type I half logistic generalized Rayleigh (TIHLGR)). We investigate some of its mathematical and statistical properties such as the explicit form of the ordinary moments, moment generating function, conditional moments, Bonferroni and Lorenz curves, mean deviations, residual life and reversed residual functions, Shannon entropy and Renyi entropy. The maximum likelihood method is used to estimate the model parameters. Simulation studies were conducted to assess the finite sample behavior of the maximum likelihood estimators. Finally, we illustrate the importance and applicability of the model by the study of two real data sets.