Alpha logarithm transformed fréchetdistribution: Properties and estimation

Abstract

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr echet (ALTF) distribution is introduced which o ers a more exible distribution for modeling lifetime data. Various properties of the proposed distribu- tion, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R enyi and -entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new dis- tribution 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 pro- posed 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.