A novel distribution with upside down bathtub shape hazard rate: properties, estimation and applications

TL;DR

This paper introduces a new statistical distribution with an upside-down bathtub hazard rate, explores its properties, estimation methods, and demonstrates its application using real data and simulations.

Contribution

The paper presents a novel distribution with specific hazard properties, derives its mathematical characteristics, and develops estimation techniques including Bayesian and maximum likelihood methods.

Findings

Distribution exhibits upside-down bathtub hazard rate shape

Maximum likelihood and Bayesian estimates are derived and validated

Real data applications demonstrate the distribution's practical utility

Abstract

In this communication, we introduce a new statistical model and study its various mathematical properties. The expressions for hazard rate, reversed hazard rate, and odd functions are provided. We explore the asymptotic behaviors of the density and hazard functions of the newly proposed model. Further, moments, median, quantile, and mode are obtained. The cumulative distribution and density functions of the general $k$th order statistic are provided. Sufficient conditions, under which the likelihood ratio order between two inverse generalized linear failure rate (IGLFR) distributed random variables holds, are derived. In addition to these results, we introduce several estimates for the parameters of IGLFR distribution. The maximum likelihood and maximum product spacings estimates are proposed. Bayes estimates are calculated with respect to the squared error loss function. Further, asymptotic confidence and Bayesian credible intervals are obtained. To observe the performance of the proposed estimates, we carry out a Monte Carlo simulation using $R$ software. Finally, two real-life data sets are considered for the purpose of illustration.