Truncated Modified Weibull: Estimation and Predication Based on Maximum Likelihood Method

Abstract

In this paper, a truncated modified Weibull distribution is introduced as a lifetime distribution, where all the parameters and the truncated points are unknown. Theprobability density function, cumulative distribution function, reliability, hazard rate and reversed hazard rate functions are obtained with graphical description. Some of its statisticalproperties including quantiles, mode,moments, moment generating function and order statistics are presented. The parameters, reliability and hazard rate functions are estimated using the maximum likelihood method. Maximum likelihood prediction of some future observations from the truncated modified Weibull distribution is considered. Finally,simulation study and a real data applicationare carried out to illustrate the theoretical results