On Bivariate Generalized Linear Failure Rate-Power Series Class of Distributions

TL;DR

This paper introduces a new, more general class of bivariate lifetime distributions called the bivariate generalized linear failure rate power series model, which encompasses several existing models and offers improved data fitting.

Contribution

It proposes a novel, flexible bivariate distribution class that generalizes existing models and provides estimation procedures and real data application.

Findings

The new model includes several existing lifetime distributions as special cases.

Maximum likelihood estimation is developed for the model parameters.

Application to real data shows better fit compared to other models.

Abstract

Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions. We refer to this new class of distributions as bivariate generalized linear failure rate power series model. This new class of bivariate distributions contains several lifetime models such as: generalized linear failure rate-power series, bivariate generalized linear failure rate and bivariate generalized linear failure rate geometric distributions as special cases among others. The construction and characteristics of the proposed bivariate distribution are presented along with estimation procedures for the model parameters based on maximum likelihood. The marginal and conditional laws are also studied. We present an application to the real data set where our model provides a better fit than other models.