Statistics Toolbox™

copulastat - Copula rank correlation

Syntax

R = copulastat('Gaussian',rho)
R = copulastat('t',rho,NU)
R = copulastat(family,alpha)
R = copulastat(...,'type',type)

Description

R = copulastat('Gaussian',rho) returns the Kendall's rank correlation R that corresponds to a Gaussian copula having linear correlation parameters rho. If rho is a scalar correlation coefficient, R is a scalar correlation coefficient corresponding to a bivariate copula. If rho is a p-by-p correlation matrix, R is a p-by-p correlation matrix.

R = copulastat('t',rho,NU) returns the Kendall's rank correlation R that corresponds to a t copula having linear correlation parameters rho and degrees of freedom NU. If rho is a scalar correlation coefficient, R is a scalar correlation coefficient corresponding to a bivariate copula. If rho is a p-by-p correlation matrix, R is a p-by-p correlation matrix.

R = copulastat(family,alpha) returns the Kendall's rank correlation R that corresponds to a bivariate Archimedean copula with scalar parameter alpha. family is one of 'Clayton', 'Frank', or 'Gumbel'.

R = copulastat(...,'type',type) returns the specified type of rank correlation. type is 'Kendall' to compute Kendall's tau, or 'Spearman' to compute Spearman's rho.

copulastat uses an approximation to Spearman's rank correlation for some copula families when no analytic formula exists. The approximation is based on a smooth fit to values computed using Monte-Carlo simulations.

Example

Get the theoretical rank correlation coefficient for a bivariate.

% Gaussian copula with linear correlation parameter rho
rho = -.7071;
tau = copulastat('gaussian',rho)
tau =
   -0.5000

% Generate dependent beta random values using that copula
u = copularnd('gaussian',rho,100);
b = betainv(u,2,2);
 
% Verify that the sample has a rank correlation
% approximately equal to tau
tau_sample = corr(b,'type','k')
tau_sample =
    1.0000   -0.5265
   -0.5265    1.0000

See Also

copulacdf, copulaparam, copulapdf, copularnd

copulapdf

copularnd