Documentation

copulapdf

Copula probability density function

Syntax

  • y = copulapdf('Gaussian',u,rho)
  • y = copulapdf('t',u,rho,nu)
  • y = copulapdf(family,u,alpha) example

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.

example

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

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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')

Related Examples

Input Arguments

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u — Values at which to evaluate pdfmatrix 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 parametersscalar 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 freedompositive 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

Data Types: single | double

alpha — Bivariate Archimedian copula parameterscalar value

Bivariate Archimedian 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

Output Arguments

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y — Probability density functionvector of scalar values

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

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