copulastat

Copula rank correlation

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Syntax

r = copulastat("Gaussian",rho)
r = copulastat("t",rho,nu)
r = copulastat(family,alpha)
r = copulastat(___,Type=CorrType)

Description

r = copulastat("Gaussian",rho) returns the Kendall’s rank correlation, r, that corresponds to a Gaussian copula with linear correlation parameters rho.

example

r = copulastat("t",rho,nu) returns the Kendall’s rank correlation, r, that corresponds to a t copula with linear correlation parameters, rho, and degrees of freedom parameter, nu.

r = copulastat(family,alpha) returns the Kendall’s rank correlation, r, that corresponds to a bivariate Archimedean copula that has the type specified by family and scalar parameter alpha.

r = copulastat(___,Type=CorrType) specifies the input rank correlation type to use, using any of the input argument combinations in the previous syntaxes.

Examples

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Open Live Script

Compute the rank correlation for a Gaussian copula with the specified linear correlation parameter rho.

rho = -.7071;
tau = copulastat('gaussian',rho)
tau = 
-0.5000

Use the copula to generate dependent random values from a beta distribution that has parameters a and b equal to 2.

rng default  % For reproducibility
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 = 2×2

    1.0000   -0.5135
   -0.5135    1.0000

Input Arguments

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Linear correlation parameters for the copula, specified as a scalar value or matrix of scalar values.

  • If rho is a scalar correlation coefficient, then r is a scalar correlation coefficient corresponding to a bivariate copula.

  • If rho is a p-by-p correlation matrix, then r is a p-by-p correlation matrix.

Data Types: single | double

Degrees of freedom for the t copula, specified as a positive integer value.

Data Types: single | double

Bivariate Archimedean copula family, specified as one of the following.

"Clayton"Clayton copula
"Frank"Frank copula
"Gumbel"Gumbel copula

Bivariate Archimedean copula parameter, specified as a scalar value. Permitted values for alpha depend on the specified copula family.

Copula FamilyPermitted Alpha Values
"Clayton"[0,∞)
"Frank"(-∞,∞)
"Gumbel"[1,∞)

Data Types: single | double

Type of rank correlation, specified as one of the following.

  • "Kendall" — Compute Kendall’s tau.

  • "Spearman" — Compute Spearman’s rho (rank correlation).

copulastat uses an approximation to Spearman’s rank correlation for copula families that do not have an existing analytic formula. The approximation is based on a smooth fit to values computed at discrete values of the copula parameters. For a t copula, the approximation is accurate for degrees of freedom larger than 0.05.

Output Arguments

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Copula rank correlation, returned as a scalar value or matrix of scalar values.

  • If rho is a scalar correlation coefficient, then r is a scalar correlation coefficient corresponding to a bivariate copula.

  • If rho is a p-by-p correlation matrix, then r is a p-by-p correlation matrix.

Version History

Introduced in R2006a

See Also

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