Discretization of the Alpha Power Weibull-G Family of Distributions: A Novel Discrete Distribution with Properties, Estimation, and Applications to Medical and Educational Data

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Abstract
This article introduces a new four-parameter discrete distribution, named the discrete alpha power Weibull-exponential (DAPWE) distribution. The new distribution is obtained by applying the survival discretization method to the alpha power Weibull-G family of distributions. The new distribution is highly flexible due to its ability to exhibit symmetric and asymmetric shapes of its probability mass function. Additionally, the hazard function exhibits various shapes including uniform, increasing, decreasing, J-shaped, reversed J-shaped and bathtub showing its versatility. Furthermore, some important characteristics of the proposed distribution, such as moments, order statistics and entropy are discussed. The method of maximum likelihood approach is used to estimate the distribution’s unknown parameters. The efficiency of the maximum likelihood in estimating the model’s parameters is assessed through simulation studies. The model performance is also evaluated through four real medical and educational data sets. The results demonstrate that the suggested distribution can indeed provide a better fit to the data compared to other distributions.

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