Modeling The Odd Moment Exponential-G Poisson Family of Distributions With Failure Time Data

Abstract

A univariate generalized family of continuous distributions, tentatively called the odd moment exponential-G Poisson family
of distribution, has been introduced in this article. Among various techniques, the framework of compounding has been employed to
devise the odd moment exponential-G distribution with the truncated Poisson distribution. With exponential distribution as a key model
of the new family, the resultant model has been studied in lieu with theoretical and applied way. The theoretical foundation has been set
up including definite mathematical expressions for shapes of density and hazard function, moments and related generating functions,
process of residual life and its regeneration, ordered statistics, mechanics of material expressed in stress-strength expressions, Rnyi
entropy and mean deviation among others. The estimation of the model parameters is performed by the maximum likelihood method
for complete and censored scenario. A simulation study (for un-censored and censored case) is carried out under varying sample sizes
to assess the efficacy of the model parameters. Three applications to the failure time data sets related to system reliability are used to
showcase the extensibility of the proposed family. The postulated distribution is anticipated to be adaptable enough to model data sets in circumstances where both entire (un-censored) and partial information (censored) is accessible.