Alpha logarithm transformed fréchet distribution: Properties and estimation

Abstract

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fréchet (ALTF) distribution is introduced which offers a more flexible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function Rényi and δ-entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.