Weibull Generalized Rayleigh Distribution: Properties and Applications

Abstract

In many practical scenarios, standard probability distributions fall short in modeling complex data structures, particularly in real life data, financial markets, and biological data, etc. To address this gap, we introduce a novel custom probability distribution tailored to real life datasets. This study introduces a novel univariate continuous probability distribution with four parameters, named the Weibull Generalized Rayleigh (WGRL) distribution. This new distribution is formulated by combining the Weibull-H class and the Generalized Rayleigh (GR) distribution. Various statistical properties, including moments, and order statistics. Utilizing the least squares method, Cramer-Von Misses approach, and maximum likelihood estimation, the parameters are computed. A real data set called "the number of deaths per day due to Covid-19 in Nepal during the first wave" is gathered in order to demonstrate the applicability of the model. P-P and Q-Q plot analysis is used to evaluate the model's validity. Some information criteria are used for model comparisons. This work aims to create a novel probability model to get more flexible, innovative and applicable to modern real datasets. We demonstrate that this new distribution outperforms traditional models in terms of fit accuracy, predictive power, and applicable in real life through both theoretical analysis and empirical validation using two real data sets. Model defined here may be useful in studying the characteristics; applications and method of knowing the custom probability model. Statistics from Anderson Darling, Cramer-Von Mises, and Kolmogorov-Smirnov are utilized to assess the suggested model's goodness of fit. R-programming language performs all computations and analysis tasks.