The Compound Class of Linear Failure Rate-Power Series Distributions: Model, Properties and Applications

TL;DR

This paper introduces a new flexible class of distributions called LFRPS, which generalizes existing models by combining linear failure rate and power series distributions, with applications in hazard rate modeling and data fitting.

Contribution

The paper proposes the LFRPS distribution class, encompassing several new and existing distributions, and discusses their properties, estimation methods, and practical data fitting applications.

Findings

LFRPS distributions can model various hazard rate shapes.

Maximum likelihood estimation via EM algorithm is developed.

Real data fitting demonstrates the model's flexibility.

Abstract

We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class of distributions. Some former works such as exponential-power series (EPS) class of distributions, exponential geometric (EG) distribution, exponential Poisson (EP) distribution and exponential logarithmic (EL) distribution are special cases of the new proposed model. The ability of the LFRPS class of distributions is in covering five possible hazard rate function i.e., increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of the LFRPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this paper. In order to show the flexibility and potentiality of the new class of distributions, the fitted results of the new class of distributions and some its submodels are compared using a real data set.