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

Deepthi  K S; Chacko V M

doi:10.64060/JASR.v1i3.1

Authors

Deepthi K S Department of Economics and Statistics, Government of Kerala, India Author
Chacko V M Department of Statistics, St. Thomas' College (Autonomous), Thrissur, Kerala, India Author https://orcid.org/0000-0002-7536-2626

DOI:

https://doi.org/10.64060/JASR.v1i3.1

Keywords:

KM-Transformation, PGKM Transformation, Exponential distribution, Bathtub shaped failure rate, Reliability

Abstract

A more useful transformation model, KM Transformation, for reliability and lifetime data analysis is introduced by Kavya & Manoharan (2021). Power generalization technique is the best approach for analysing a parallel system. In this article, we present a new transformation called Power Generalized KM-Transformation (PGKM) to obtain a more appropriate model while monotone and non-monotone behaviour for the failure rate function occurs. We derived the moments, moment generating function, characteristic function, quantiles, etc. for the PGKM transformation of Exponential distribution (PGKME). Distributions of minimum and maximum are obtained. Estimation of parameters of the PGKME distribution is performed via maximum likelihood method, method of moment, and least square estimation method. A simulation study is performed to validate the maximum likelihood estimator (MLE). Analysis of three sets of real data is provided.

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