Advances in new continuous distributions and families : theoretical methods and applications

Abstract

Classical distributions such as exponential, Weibull, Burr XII, log-logistic, and beta have been widely used to model various types of data in different fields. However, with the development of computer science, more flexible distributions are needed to deal with increasingly complex data sets. In the last three decades, several studies have proposed new flexible distributions, adding more parameters to the existing ones using distribution generators such as MarshallOlkin-G, beta-G, and Kumaraswamy-G. A revision of the gamma-G family is employed, along with four new distributions, namely, the gamma flexible Weibull, the exponentiated power Ishita, the flexible generalized gamma, and the generalized Marshall-Olkin Lomax. In addition, five new families of distributions are developed: the exponential Power-G, the Marshall-Olkin flexible generalized, the odd power Ishita-G, the modified Kies flexible generalized, and the modified odd Bur XII-G. Regression models are also implemented based on the new families and distributions, and the maximum likelihood method is adopted to estimate their parameters. Simulation studies are carried out to verify their consistency. In addition, the potential of the new models is demonstrated using real data sets, including COVID-19 data. The results show that the proposed models effectively capture the complex patterns observed in the data and outperform existing classical distributions. Overall, this work contributes to developing more flexible and accurate distributions for data modeling