Links between the Incomplete Gamma Function and the Independent and Gumbel Copulas

Abstract

To obtain the links between the incomplete gamma function and the two copulas (independent and Gumbel). We went through some integral function transformations. The transformations used are Laplace, Fourier, and Mellin. Our work can be seen as a bridge between the notion of copula in probability and Euler’s gamma function which has a lot of application in mathematical modeling. In short, a wide range of possibilities is offered to us thanks to these links that we have established.