A new approach of generalized Rayleigh distribution with analysis of asymmetric data sets

Defining a probability model suitable for analyzing intricate and skewed real datasets holds significant importance in statistics. Here In this study, a novel class of models using the maximum of independent identical generalized Rayleigh random variables with the number of variables that have a power series class of distributions is proposed. This novel family of distributions contain several sub-models, including Poisson-generalized Rayleigh, geometric-generalized Rayleigh, binomial-generalized Rayleigh, and logarithmic-generalized Rayleigh models. The so obtained model can be unimodal and positively skewed, and it can be applied in modeling asymmetric data. We provide numerous distributional and statistical properties of this new family of distribution, notably, probability density, cumulative function, hazard rate function, k-moment, mean, variance, and quantile function. Different techniques consider the estimation of model parameters, likely maximum likelihood estimators, Expectation–Maximization (EM) and its Modified techniques, and extensive Monte Carlo (MC) simulation studies have been employed to see the efficiency of the suggested estimation techniques. At the end, three real data sets are analyzed for illustrative purposes. The results underscore the superior performance of the proposed Geom-GR model compared to its competitors, showcasing its effectiveness in accurately representing the analyzed datasets.