The Discrete Power Garima-Generated Family of Distributions

In a period of fast growth in technology, there is an ongoing increase in the amount of complex data collected from many different fields. The increasing complexity of data causes a greater difficulty in properly utilizing the current probability distributions for real-world data analysis. In statistics, probability distributions are developed to suit the data. Within this framework, a flexible family of discrete models called the discrete power Garima-generated (DPGa-G) family is proposed. In this study, its statistical properties are derived and its sub-models including the DPGa-Fréchet, DPGa-Weibull, and DPGa-exponential distributions are investigated. The considered sub-models present a variety of probability function shapes, i.e., decreasing, left-skewed, right-skewed, and symmetric for different values of the proposed model’s parameters. Furthermore, the DPGa-G family of distributions has a flexible fit for represent skewed and symmetric data sets, and provides a more fit for data that is equi-, over-, and under-dispersed. Five methods of parameter estimation are studied to estimate the parameters, including Anderson–Darling, Cramer–Von Mises, least squares, weighted least squares, and maximum likelihood estimations. Furthermore, a compact Monte Carlo simulation study is used to evaluate the performance of the estimators considered using the DPGa-Fréchet distribution. The application analyzes the distribution of a dataset on the number of cysts in the kidneys of patients using the proposed distributions and their baseline distributions. The results indicate that the DPGa-G family of distributions provides a better fit than their baseline distributions.