A New Bivariate Transmuted Family of Distributions: Properties and Application

Abstract

The cubic transformation families of distributions are widely used to model complex univariate data. However, in many situations, the jointly modeling of two variables is necessary, making bivariate distributions essential. This paper introduces a novel family of bivariate probability distributions that extends the univariate cubic transformation family. The bivariate cubic transmuted (BCT) family of distributions is comprehensively discussed, with its statistical properties explored in detail. Within this family, the bivariate cubic transmuted Burr (BCTB) distribution is specifically analyzed. Its statistical properties are examined, and its parameters are estimated using the maximum likelihood estimation (MLE) method. To assess the performance of the estimation procedure, a Monte Carlo simulation study is conducted. Furthermore, the applicability of the proposed model is demonstrated by fitting it to real datasets, and its relevance is further discussed.