PairCopulaHVolume

Computing the h-volume of a copula

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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.