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

Volume 12, Issue 5, pp 262--277 Publication Date: December 13, 2018       Article History
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### Authors

M. Shrahili - Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia. I. Elbatal - Department of Mathematics and Statistics, College of Science Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia. Mustapha Muhammad - Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano (BUK), Nigeria.

### Abstract

In this paper, we explore the properties and importance of a lifetime distribution so called type I half-logistic Burr X $({\rm TIHL}_{BX})$ in detail (also called type I half logistic generalized Rayleigh $(\text{TIHL}_{GR})$). 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.

### Keywords

• Type I half logistic distribution
• Burr X distribution
• moments
• maximum likelihood estimate

•  62E05
•  62F10
•  62F12

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