Computing the h-volume of a copula
The function computes the probability for a random vector, being distributed according to a specific copula, to lie in a hyperrectangle. The hyperrectangle is defined by the cartesean product of the intervals specified by the lower bounds a and upper bounds b. Possible pair-copula families:
0 Indep 1 AMH 2 AsymFGM 3 BB1 4 BB6 5 BB7 6 BB8 7 Clayton 8 FGM 9 Frank 10 Gaussian 11 Gumbel 12 IteratedFGM 13 Joe 14 PartialFrank 15 Plackett 16 Tawn1 17 Tawn2 18 Tawn 19 t
P = CopulaHVolume(family,a,b,theta) Rotated pair-copulas P = CopulaHVolume(family,a,b,theta,rotation)
family = The copula family. a = A 2-dimensional vector of lower bounds for 2 intervals, defining a 2-dimensional hyperrectangle. b = A 2-dimensional vector of upper bounds for 2 intervals, defining a 2-dimensional hyperrectangle. theta = The parameter vector for the pair-copula. rotation = The degree of rotation, i.e., either 90, 180 or 270. No rotation is achieved by letting the rotation argument empty or by choosing 0 rotation.
P = The probability for a random variable, which is distributed according to the specified pair-copula, to lie in the hyperrectangle defined by the lower and upper bounds vectors a and b.