On bivariate Teissier model using Copula: dependence properties, and case studies

To precisely represent bivariate continuous variables, this work presents an innovative approach that emphasizes the interdependencies between the variables. The technique is based on the Teissier model and the Farlie-Gumbel-Morgenstern (FGM) copula and seeks to create a complete framework that captures every aspect of associated occurrences. The work addresses data variability by utilizing the oscillatory properties of the FGM copula and the flexibility of the Teissier model. Both theoretical formulation and empirical realization are included in the evolution, which explains the joint cumulative distribution function F(z1,z2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {F}(z_{1}, z_{2})$$\end{document}, the marginals F(z1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {F}(z_{1})$$\end{document} and F(z2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {F} (z_{2})$$\end{document}, and the probability density function (PDF) f(z1,z2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {f}(z_{1},z_{2})$$\end{document}. The novel modeling of bivariate lifetime phenomena that combines the adaptive properties of the Teissier model with the oscillatory characteristics of the FGM copula represents the contribution. The study emphasizes the effectiveness of the strategy in controlling interdependencies while advancing academic knowledge and practical application in bivariate modelling. In parameter estimation, maximum likelihood and Bayesian paradigms are employed through the use of the Markov Chain Monte Carlo (MCMC). Theorized models are examined closely using rigorous model comparison techniques. The relevance of modern model paradigms is demonstrated by empirical findings from the Burr dataset.