An Extension of the Generalized Linear Failure Rate Distribution

TL;DR

This paper introduces a new flexible extension of the generalized linear failure rate distribution, capable of modeling various hazard rate shapes and applicable to lifetime data analysis.

Contribution

It presents a novel extended distribution that encompasses several known lifetime distributions and explores its statistical properties and parameter estimation methods.

Findings

The new distribution can model various hazard rate shapes including decreasing, increasing, and bathtub.

Statistical properties such as moments, skewness, and kurtosis are derived.

Application to real data demonstrates its usefulness in lifetime data analysis.

Abstract

In this paper, we introduce a new extension of the generalized linear failure rate distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and generalized linear failure rate distributions as special sub-models. In addition, it can have a constant, decreasing, increasing, upside-down bathtub (unimodal), and bathtub-shaped hazard rate function depending on its parameters. We provide some of its statistical properties such as moments, quantiles, skewness, kurtosis, hazard rate function, and reversible hazard rate function. The maximum likelihood estimation of the parameters is also discussed. At the end, a real data set is given to illustrate the usefulness of this new distribution in analyzing lifetime data.