How to Cite
Abstract
Abstract: In this paper, we investigate the distribution of the sum of two dependent random variables whose marginal densities are known. The dependence structure between the variables is modeled using a copula function. Based on Sklar’s theorem, we derive an explicit integral representation for the probability density function of the sum. The obtained result generalizes the classical convolution formula for independent random variables and provides a flexible framework for modeling dependence in applied probability and statistics [1], [2].
References
1. Nelsen, R. B. An Introduction to Copulas. Springer.
2. Joe, H. Dependence Modeling with Copulas. Chapman & Hall. 2014. CRC Press.
3. Sklar, A. Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 1959.
4. Schweizer, B., Sklar, A. Probabilistic Metric Spaces. Dover.
5. Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall, London.
6. Durante, F., Sempi, C. Principles of Copula Theory. CRC Press.