# PairCopulaHVolume

Computing the h-volume of a copula

## Purpose

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
``````

## Usage

``````           P = CopulaHVolume(family,a,b,theta)
Rotated pair-copulas
P = CopulaHVolume(family,a,b,theta,rotation)
``````

## Inputs

``````   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.
``````

## Outputs

``````  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.
``````