The Kumaraswamy Generalized Inverse Lomax distribution and applications to reliability and survival data

Abstract

In this paper, a new four-parameter distribution is developed and studied using the tractability properties of the Kumaraswamy generalized family of distributions and the features of the Inverse Lomax distribution. The newly developed distribution is called the Kumaraswamy Generalized Inverse Lomax distribution. We derive its main probability and reliability functions and examine its modeling behavior by considering different parameter combinations. Expectedly, the corresponding hazard rate function is very flexible; it possesses increasing, decreasing, and inverted (upside-down) bathtub shapes. Some important characteristics of the Kumaraswamy Generalized Inverse Lomax distribution are derived, including moments, incomplete moments, stress-strength reliability, probability weighted moments, Renyi and Tsallis entropy measures, order statistics, moment generating function, mean residual life, and mean activity time. The maximum likelihood estimation technique is used to obtain an estimate of the parameters of the new model, and a brief simulation study shows its effectiveness. The application of the new model is based on three real-life data sets used to show the modeling potential of the proposed distribution. The Kumaraswamy Generalized Inverse Lomax distribution turns out to be best by capturing important details in the structure of the data considered.