Proportional Hazard Inverse Weibull Distribution and Associated Inference

Abstract

In this study, we have considered the proportional hazard version of the inverse Weibull distribution. It has been shown that the density and hazard rate functions are unimodal and the mean residual life function is bathtub shaped. For the considered model, many functions of the parameters, such as the mean, variance, coefficient of variation and the critical points of the density, hazard rate and mean residual life functions cannot be given in explicit form. As a result, the variances of the maximum likelihood estimators of such functions cannot be given in explicit form to construct the usual asymptotic confidence interval. In this study, we use the percentile bootstrap estimation method to estimate such variances to construct the asymptotic confidence intervals. The asymptotic confidence intervals are compared with the bootstrap confidence intervals. Simulation studies are carried out to examine the performance of the maximum likelihood and bootstrap estimators. An example is provided to illustrate the procedure.