The Proportional Hazard Generalized Power Weibull Distribution: Properties, Applications and Regression Model

We introduce the proportional hazard generalized power Weibull (PHGPW) model in which hazard rate function can assume increasing, decreasing, unimodal or (upside bathtub) and constant. Some of its mathematical properties are studied including the power series for the quantile function. Monte Carlo simulation was performed to determine the finite sample behaviour of the maximum likelihood estimates of the parameters. The flexibility of the PHGPW distribution compared with some other existing distributions is proved empirically by means of two sets of real data related to remission times of bladder cancer patients and strike duration of manufacturing company. A new regression model was defined based on the PHGPW distribution. The performance of the regression model is proved empirically using real data set.