Type II Half Logistic Rayleigh Distribution: Properties and Estimation Based on Censored Samples
Muhammad Ahsan Ul Haq
Quality Enhancement Cell, National College of Arts (NCA), Lahore, Pakistan.
Abdullah M. Almarashi
Department of Statistics, Faculty of Science, King Abdul-Aziz University, Jeddah, Kingdom of Saudi Arabia.
Amal S. Hassan *
Department of Mathematical Statistics, Institute of Statistical Studies and Research (ISSR), Cairo University, Egypt.
M. Elgarhy
Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, Kingdom of Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce a new model called the Type II half logistic Rayleigh (TIIHLR) with U-shaped, increasing and decreasing hazard rate function. Some structural properties of the current distribution are derived including; explicit expressions for moments, incomplete moments, order statistics and Rényi entropy. Maximum likelihood estimators of the model parameters, based on complete and censored samples, are obtained. A numerical study is demonstrated to illustrate the theoretical results. The superiority of the new model over some new existing distributions is illustrated through two real data sets. In both applications, the TIIHLR model produces better fits than; the transmuted Rayleigh; transmuted generalised Rayleigh; exponentiated transmuted generalised Rayleigh and transmuted exponentiated inverse Rayleigh distributions.
Keywords: Maximum likelihood method, order statistics, Rayleigh distribution, type II half logistic family