Abstract
This paper compares the performance of some Archimedean Copulas in approximating the bivariate skew-normal distribution. Our study shows Frank Copula is a better Archimedean Copula for approximating the bivariate skew-normal distribution.
Highlights
It has been noted in many applications that skewness is very prevalent in many univariate distributions which includes the family of normal distributions
We investigate the possibility of fitting an Archimedean Copulas for the bivariate skew-normal density function
Construction of Skew-Gaussian Copula: we investigate the properties of the skew-normal and the bivariate skew-normal distributions
Summary
It has been noted in many applications that skewness is very prevalent in many univariate distributions which includes the family of normal distributions. Where x and x are the density function and the cumulative probability distribution function for the standard normal distribution respectively This skew-normal distribution and its applications have been studied extensively by Azzalini (1985, 1986), Henze (1986) and Quiroga (1992). The interest is in finding the best Archimedean Copula that approximates the bivariate skew-normal distribution when the marginal distributions are skew-normal distributions. Krazanowski (1988) point out the need for alternatives to the normal distribution especially in actuarial science This is an area where the copula models could fill the void. We investigate the possibility of fitting an Archimedean Copulas for the bivariate skew-normal density function. Our research shows that “Frank Copula” is the best fitting Archimedean Copula for the bivariate skew-normal density function
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