POWER GENERALIZED DUS TRANSFORMATION IN WEIBULL AND LOMAX DISTRIBUTIONS

Abstract

A strong need for an appropriate lifetime model arises in reliability analysis. A large number of lifetime distributions are available in the literature. To analyze reliability data, a more suitable lifetime distribution is plausible. Power Generalized DUS (PGDUS) transformation of the lifetime model gives a solution to fit the data with more precision. PGDUS transformation of the exponential distribution is the first attempt in this regard. This new class of distributions can be used for model series systems in which the components are distributed as DUS transformations of some lifetime model. This paper introduces two novel classes of distributions using PGDUS transformation, which is a generalization of DUS transformation, with Weibull and Lomax distributions as the baseline distributions. Some analytical properties like moments, moment generating function, characteristic function, cumulant generating function, quantile function, distribution of order statistics, and Rényi entropy are derived. The maximum likelihood estimation procedure is employed to estimate the unknown parameters. Moreover, a simulation study has been conducted, and data has been analyzed for each of the proposed distributions to demonstrate how well the distributions would perform in a real-life situation. In comparison with some other recent new models, the proposed distribution is found to be a better model.