The New Strange Generalized Rayleigh Family: Characteristics and Applications to COVID-19 Data

Abstract

In this paper, we introduce a novel family of continuous distributions known as the Odd Generalized Rayleigh-G Family. Within this family, we present a special sub-model known as the odd Generalized Rayleigh Inverse Weibull (OGRIW) distribution. The OGRIW distribution is derived by combining the T-X family and the Generalized Rayleigh distribution. We provide a comprehensive expansion of the (PDF) and (CDF) for the OGRIW distribution. Additionally, we investigate several mathematical properties of the OGRIW distribution, including moments, moment-generating function, incomplete moments, quantile function, order statistics and Rényi entropy. To estimate the model parameters, we employ the maximum likelihood method, aiming to identify the parameter values that maximise the likelihood of the observed data.

Finally, we apply the proposed OGRIW distribution to two real COVID-19 datasets from Mexico and Canada. The results of these applications demonstrate that the new distribution exhibits remarkable flexibility and outperforms other comparative distributions in terms of accurately modelling the COVID-19 data.