An intermediate muth distribution with increasing failure rate

Abstract

In the context of reliability theory, Eginhard J. Muth introduced in 1977 a continuous probability distribution that has been overlooked in the statistical literature. This paper is devoted to that model. Some statistical measures of the distribution are expressed in closed form and it is shown that the model has increasing failure rate and strictly positive memory. Moreover, the members of this family of distributions can be ordered in terms of the hazard rate order. With respect to the parameter estimation, a problem of identifiability was found via Monte Carlo simulation, which is due to the existence of two shape parameters. Such a problem is overcome if one of the parameters is assumed to be known and then the maximum likelihood method provides accurate estimates. Rainfall data sets from the Australian Bureau of Meteorology are used to illustrate that the model under consideration may be an interesting alternative to other probability distributions commonly used for modeling non-negative real data. © 2021 Taylor & Francis Group, LLC.