A Discrete Analogue of the Exponentiated Generalized Weibull-G Family: A New Discrete Distribution with Different Methods of Estimation and Application

Statistical distributions play a crucial role in analyzing real data with varying behavior. In this study, the exponentiated generalized Weibull-G family is discretized using the survival discretization method. Furthermore, a three-parameter discrete distribution, called the exponentiated generalized Weibull–Rayleigh distribution, is generated from this discretized family. This distribution is flexible in modeling various data types, as evidenced by the distinct structures of its probability mass function and hazard rate function. Some statistical properties of both the family and the proposed distribution are discussed. Three estimation approaches—the maximum likelihood, the minimum chi-square, and the method of moments—are used to estimate the distribution’s parameters and are evaluated across three simulation cases. Moreover, the effectiveness of the proposed distribution is evaluated using four datasets from medicine and education. Overall, the results demonstrated the superiority of the proposed distribution fitting the examined data relative to some existing discrete models.