Statistical Inference of Odd Fréchet Inverse Lomax Distribution with Applications

In this article, we propose and study a new three-parameter distribution, called the odd Fréchet inverse Lomax (OFIL) distribution, derived by combining the odd Fréchet-G family and the inverse Lomax distribution. Since Fréchet is a continuous distribution with wide applicability in extreme value theory, the new model contains these properties as well as the characteristics of the inverse Lomax distribution which make it more flexible and provide a good alternative for some well-known lifetime distributions. We initially present a linear representation of its functions and discussion on density and hazard rate function. Then, we study its various mathematical properties. Different estimation methods are used to estimate parameters of OFIL. The Monte Carlo simulation study is carried out to compare the efficiencies of different methods of estimation. The maximum likelihood estimation (MLE) method is used to estimate the OFIL parameters by considering three practical data applications. We show that the related model is the best in comparisons based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and other goodness-of-fit measures.