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On bivariate modelling using a new statistical distribution with homogeneous marginals

Recent studies have shown that the univariate exponentiated Teissier distribution is an effective model for analysing rainfall data. A bivariate probability distribution offers greater insight into a process like a flood or drought than a univariate method for analysing the characteristics of environmental occurrences. As a result, in this study we developed a bivariate exponentiated Teissier distribution. The marginals of the proposed distribution model follow the exponentiated Teissier distribution. The cumulative distribution function of this bivariate model consists of continuous and singular components. The proposed model is shown to have several fundamental statistical properties, including joint cumulative distribution, joint density, marginals, and conditional distributions. Additionally, some copula functions are examined. The proposed model's parameter estimations are derived using the maximum likelihood method. Furthermore, the asymptotic confidence intervals are given for these estimates. A Monte Carlo simulation study with various sample sizes was performed to evaluate the behaviour of maximum likelihood estimates. Finally, we used football and flood datasets to demonstrate how the proposed model may be employed.