Modified Ramos-Louzada-G family with baseline Weibull distribution: Properties, characterizations, regression, and applications

Abstract

The paper introduced a novel family of distributions, called the Kumaraswamy Ramos-Louzada-G (KumRL-G) class, focusing on the five-parameter Kumaraswamy Ramos-Louzada Weibull (KumRLW) distribution. This new family of distributions, which includes existing and numerous new sub-models, offers improved flexibility and accuracy in modeling and analyzing survival data. Key statistical properties, including quantile function, moments, and entropy measures underlying the distribution have been derived, and characterizations have also been provided based on the ratio of two truncated moments and the hazard rate function. The maximum likelihood estimation (MLE) is employed to estimate the parameters of the proposed probability distribution, and Monte Carlo simulation analysis is performed to demonstrate the effectiveness of this method. The significance and adaptability of the new family of distributions are revealed through applications to COVID-19 and survival rate to age 65 of male cohort datasets from Ghana, Nigeria, and Canada. A new location-scale regression model was subsequently formulated from the new KumRLW distribution. Its practicality was demonstrated using survival data on hypertension from Ghana with gender as a covariate. The regression analysis showed that gender is a significant factor in the length of time before hypertension develops. The new KumRL-G family with baseline Weibull distributions provides more flexibility and improved fit in modeling various shapes and behaviors in the survival datasets surpassing its existing sub-models and other notable distributions.