Compounded Linear Failure Rate Distribution: Properties, Simulation and Analysis

TL;DR

This paper introduces a new extended linear failure rate distribution with an extra shape parameter, enhancing modeling flexibility for lifetime data, supported by theoretical properties, simulation, and real data analysis.

Contribution

It proposes a novel extension of the LFR model with an additional shape parameter, providing more flexible hazard rate functions and comprehensive statistical properties.

Findings

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

Simulation studies show the estimators perform well.

Real data applications demonstrate the model's superiority over classical alternatives.

Abstract

This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time from a set of LFR distributed variables. We define the model, derive certain statistical properties such as the mean residual life, the mean inactivity time, moments, quantile, order statistics and also discuss the results on stochastic orders of the proposed distribution. The proposed model has increasing, bathtub shaped and inverse bathtub shaped hazard rate function. We use the method of maximum likelihood estimation to estimate the unknown parameters. We conduct simulation studies to examine the behavior of the estimators. We also use three real datasets to evaluate the model, which turns out superior compared to classical alternatives.