A New Class of Distributions with Applications to Complete Data and Survival Data with Long-Term Survivors

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper aims to propose a new class of distributions called the exponential power power series (EPPS) class of distributions. The hazard function of the proposed class can be increasing, decreasing, modified bathtub (increasing-decreasing-increasing) and bathtub shaped. Among others, the exponential power geometric (EPG) distribution is presented as a special case of the proposed family. A defective version of EPG distribution is defined to estimate the fraction of long-term survivors in a population. The moments of the defective EPG distribution are obtained. More importantly, owing to the proposed defective distribution, a cure rate regression model is proposed for modelling lifetime data contains long-term survivors with associated covariates. The maximum likelihood method and Bayesian method are used for estimating the unknown parameters. The performance of these estimation methods is examined by conducting a simulation study. The importance of the proposed family is illustrated by means of three distinctive real data sets