The Equilibrium Renewal Burr XII Distribution: Properties and Applications
Abdulzeid Yen Anafo *
Department of Mathematical Sciences, University of Mines and Technology, Ghana.
Lewis Brew
Department of Mathematical Sciences, University of Mines and Technology, Ghana.
Suleman Nasiru
Department of Statistics, C.K. Tedam University of Technology and Applied Sciences, Ghana.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.
Keywords: Equilibrium renewal process, Burr XII distribution, maximum Likelihood estimation, simulation, remission, hazard function and cancer data