Title: A copula-based measure of asymmetry between the lower and upper tail probabilities of bivariate distributions
Authors: Shogo Kato - The Institute of Statistical Mathematics (Japan) [presenting]
Toshinao Yoshiba - Tokyo Metropolitan University (Japan)
Shinto Eguchi - The Institute of Statistical Mathematics (Japan)
Abstract: A measure of asymmetry between the lower and upper tail probabilities of bivariate distributions is proposed. The expression for the proposed measure can be simplified if bivariate distribution functions are represented using copulas. With this representation, it is seen that the proposed measure possesses some desirable properties as a measure of asymmetry. The limit of the proposed measure as the index goes to the boundary of its domain can be expressed in a simple form under certain conditions on copulas. A sample analogue of the proposed measure for a sample from a copula is presented and its weak convergence to a Gaussian process is shown. Another sample analogue of the presented measure is given, which is based on a sample from the original bivariate distribution on the plane. Simple methods for interval estimation are presented. As an example, the presented measure is applied to stock daily returns of S\&P500 and Nikkei225.