Journal of Statistics Applications & Probability
Abstract
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.
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/jsap/110205
Recommended Citation
M. E. Abd El-Monsef, M.; M. El-Awady, M.; and M. Seyam, M.
(2022)
"A New Class of Distributions with Applications to Complete Data and Survival Data with Long-Term Survivors,"
Journal of Statistics Applications & Probability: Vol. 11:
Iss.
2, Article 5.
DOI: http://dx.doi.org/10.18576/jsap/110205
Available at:
https://digitalcommons.aaru.edu.jo/jsap/vol11/iss2/5