Power Generalized KM-Transformation for Non-Monotone Failure Rate Distribution

TL;DR

This paper introduces the Power Generalized KM-Transformation (PGKM), a new lifetime distribution model capable of representing both monotone and non-monotone hazard rates, with derivations, estimation methods, and real data applications.

Contribution

It proposes the PGKM model, extending KM-transformation with power generalization to handle diverse hazard rate behaviors in lifetime data.

Findings

The PGKM model captures various hazard rate shapes.

Maximum likelihood estimators are validated through simulation.

Real data analysis demonstrates the model's applicability.

Abstract

Lifetime models with a non-monotone hazard rate $\hspace{0.12cm}$ function have a wide range of applications in engineering and lifetime data analysis. There are different bathtub shaped failure rate models that are available in reliability literature. Kavya and Manoharan (2021) introduced a new transformation called KM-transformation which was found to be more useful in reliability and lifetime data analysis. Power generalization technique would be the best approach to deal with a system whose components are connected in series, in which the distribution of the component is KM-transformation of any lifetime model. In this article, we introduce a new lifetime model, Power Generalized KM-Transformation (PGKM) for Non-Monotone Failure Rate Distribution, which shows monotone and non-monotone behavior for the hazard rate function for different choices of values of parameters. We derive the moments, moment generating function, characteristic function, quantiles, entropy etc of the proposed distribution. Distributions of minimum and maximum are obtained. Estimation of parameters of the distribution is performed via maximum likelihood method. A simulation study is performed to validate the maximum likelihood estimator (MLE). Analysis of three sets of real data are given.