The Generalized Fréchet Distribution with Variable Hazard Rate Shapes: Properties and Applications

Abstract

A new five-parameter model called the generalized linear failure rate Fréchet (GLFRF) distribution is studied. The GLFRF distribution provides monotone and nonmonotone hazard rate shapes including bathtub, modified bathtub and unimodal shapes which are very common in applied fields. Some mathematical properties of the GLFRF model such as quantile function, ordinary and incomplete moments, order statistics, generating function, moments of residual and reversed resedual lifes are derived. The density function of the GLFRF distribution can be expressed as a linear combination of Fréchet densities. The maximum likelihood approach is adopted to estimate the GLFRF parameters. The flexibility of the new distribution is proved empirically using two real-life data sets. The GLFRF distribution provides better fit as compared to the Kumaraswamy–Fréchet, Kumaraswamy Marshall–Olkin Fréchet, beta-Fréchet, exponentiated- Fréchet, and gamma extended-Fréchet distributions.