Statistical theory and practice of the inverse power Muth distribution

Abstract

The Muth distribution and its derivation have been used to construct numerous statistical models in recent years, with applications in a variety of fields. In this paper, we use the inverse scheme to introduce the inverse power Muth distribution. It thus constitutes a new three-parameter heavy-tailed lifetime distribution belonging to the family of inverse distributions, which does not appear to have received adequate attention in the literature. We naturally call it inverse power Muth distribution. Two complementary parts compose the article. The first part aims to determine the main statistical properties of the inverse power Muth distribution, such as the shape behavior of the probability density and hazard rate functions, the expression of the quantile function and the related quantities, and some moment measures. The second part is devoted to its practical aspects, with a focus on its modeling capabilities. We examine the estimation of the model parameters via several well-established methods, including classical and Bayesian estimation methods. Then, we illustrate the flexibility and potential usefulness of the inverse power Muth model by means of a simulation study and two real datasets. A fair investigation reveals that it can outperform existing and comparable three-parameter models also based on the inverse scheme.