Bivariate Truncated Burr–Weibull Distribution: Properties and Application

The modeling of complex data has garnered significant interest among researchers, leading to the development of novel probability distributions. Joint modeling of two variables introduces additional challenges, necessitating the use of bivariate distributions. The field of bivariate distribution development remains relatively nascent, particularly for truncated distributions, which are essential in situations where data domains are restricted. While univariate truncated distributions have been extensively studied, their bivariate counterparts remain largely unexplored. In this paper, we propose a new bivariate distribution, termed the Bivariate Truncated Burr–Weibull (BTB-W) distribution, and investigate its statistical properties in detail. These include the marginal and conditional distributions, product and ratio moments, and conditional moments. Parameter estimation is performed using maximum likelihood techniques. The proposed BTB-W distribution is evaluated against established models, including the bivariate Burr, bivariate Lomax, bivariate log-logistic, and bivariate transmuted Weibull distributions, using real datasets. The comparative analysis, based on Akaike Information Criterion (AIC) and Bayesian Information Criterion, demonstrates that the BTB-W distribution outperforms the competing models, establishing its effectiveness and utility in complex data modeling.