Generalized Alpha-Beta-Power Family of distributions: Properties and applications

Abstract

In this article, a new family of distributions is introduced called the Generalized Alpha-Beta-Power family, applying the concept of Exponentiated family to the Alpha-Beta Power family. The family introduces three parameters to an existing model, increasing its flexibility. A special model of the family, taking exponential distribution as the baseline distribution, is studied in detail. The density curves of the distribution are found to accommodate decreasing and right-skewed heavy-tailed shapes with changes in values of the shape and scale parameters. The hazard plots can be increasing, decreasing or bath-tub shaped. Statistical properties of the distribution, like moments, moment generating function, order statistics and entropy are mathematically derived. Parameter estimation is done using the maximum likelihood estimation method, and simulation studies are used to assess the performance of the parameters. The proposed model is applied to the data sets in the field of reliability, engineering and medicine, and is compared to existing models to understand its practicality in the modeling of the probability of observations.