copulapdf

Copula probability density function

Syntax

y = copulapdf('Gaussian',u,rho)

y = copulapdf('t',u,rho,nu)

y = copulapdf(family,u,alpha)

Description

y = copulapdf('Gaussian',u,rho) returns the probability density of the Gaussian copula with linear correlation parameters, rho, evaluated at the points in u.

y = copulapdf('t',u,rho,nu) returns the probability density of the t copula with linear correlation parameters, rho, and degrees of freedom parameter, nu, evaluated at the points in u.

y = copulapdf(family,u,alpha) returns the probability density of the bivariate Archimedean copula of the type specified by family, with scalar parameter, alpha, evaluated at the points in u.

Examples

Compute the Clayton Copula pdf

Define two 10-by-10 matrices containing the values at which to compute the pdf.

u = linspace(0,1,10);
[u1,u2] = meshgrid(u,u);

Compute the pdf of a Clayton copula that has an alpha parameter equal to 1, at the values in u.

y = copulapdf('Clayton',[u1(:),u2(:)],1);

Plot the pdf as a surface, and label the axes.

surf(u1,u2,reshape(y,10,10))
xlabel('u1')
ylabel('u2')

Input Arguments

u — Values at which to evaluate pdf

matrix of scalar values in the range [0,1]

Values at which to evaluate the pdf, specified as a matrix of scalar values in the range [0,1]. If u is an n-by-p matrix, then its values represent n points in the p-dimensional unit hypercube. If u is an n-by-2 matrix, then its values represent n points in the unit square.

If you specify a bivariate Archimedean copula type ('Clayton', 'Frank', or 'Gumbel'), then u must be an n-by-2 matrix.

Data Types: single | double

rho — Linear correlation parameters

scalar values | matrix of scalar values

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

• If u is an n-by-p matrix, then rho is a p-by-p correlation matrix.

• If u is an n-by-2 matrix, then rho can be a scalar correlation coefficient.

Data Types: single | double

nu — Degrees of freedom

positive integer value

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

Data Types: single | double

family — Bivariate Archimedean copula family

'Clayton' | 'Frank' | 'Gumbel'

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

'Clayton'	Clayton copula
'Frank'	Frank copula
'Gumbel'	Gumbel copula

alpha — Bivariate Archimedean copula parameter

scalar value

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

Copula Family	Permitted Alpha Values
'Clayton'	[0,∞)
'Frank'	(-∞,∞)
'Gumbel'	[1,∞)

Data Types: single | double

Output Arguments

y — Probability density function

vector of scalar values

Probability density function, evaluated at the values in u, returned as a vector of scalar values.

Version History

Introduced in R2006a