The Power Muth Distribution

Abstract

Muth introduced a probability distribution with application in relia-bility theory. We propose a new model from the Muth law. This paper studies itsstatistical properties, such as the computation of the moments, computer generationof pseudo-random data and the behavior of the failure rate function, among others.The estimation of parameters is carried out by the method of maximum likelihoodand a Monte Carlo simulation study assesses the performance of this method. Thepractical usefulness of the new model is illustrated by means of two real data sets,showing that it may provide a better fit than other probability distributions.