Record-Based Transmuted Generalized Linear Exponential Distribution with Increasing, Decreasing and Bathtub Shaped Failure Rates

TL;DR

This paper introduces a flexible record-based transmuted generalized linear exponential distribution capable of modeling various failure rate shapes, including increasing, decreasing, and bathtub-shaped, with comprehensive statistical analysis and real data application.

Contribution

The paper proposes a new RTGLE distribution that generalizes existing models, providing better fit for diverse failure rate data and detailed statistical properties and estimation methods.

Findings

The RTGLE distribution effectively models IFR, DFR, and BTFR data.

Maximum likelihood and other estimators are developed with bias and MSE analysis.

Real data application confirms the distribution's good fit and practical utility.

Abstract

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He (2021). The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Renyi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramer-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data set based on failure time illustrates the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded.