SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17

Function summary

• multigammaln(a, d)

Functions

• multigammaln(a, d)

  returns the log of multivariate gamma, also sometimes called the
  generalized gamma. 
  
  :Parameters:
      a : ndarray
          the multivariate gamma is computed for each item of a
      d : int
          the dimension of the space of integration.
  
  :Returns:
      res : ndarray 
          the values of the log multivariate gamma at the given points a.
  
  Note
  ----
  
  The formal definition of the multivariate gamma of dimension d for a real a
  is :
  
  \Gamma_d(a) = \int_{A>0}{e^{-tr(A)\cdot{|A|}^{a - (m+1)/2}dA}}
  
  with the condition a > (d-1)/2, and A>0 being the set of all the positive
  definite matrices of dimension s. Note that a is a scalar: the integration
  is multivariate, the argument is not.
  
  This can be proven to be equal to the much friendler equation:
  
  \Gamma_d(a) = \pi^{d(d-1)/4}\prod_{i=1}^{d}{\Gamma(a - (i-1)/2)}.
  
  Reference:
  ----------
  
  R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in
  probability and mathematical statistics). 

Imported Names