lauricella {mggd} | R Documentation |
Lauricella
-Hypergeometric Function
Description
Computes the Lauricella -hypergeometric Function function.
Usage
lauricella(a, b, g, x, eps = 1e-06)
Arguments
a |
numeric. |
b |
numeric vector. |
g |
numeric. |
x |
numeric vector. |
eps |
numeric. Precision for the nested sums (default 1e-06). |
Details
If is the length of the
and
x
vectors,
the Lauricella -hypergeometric Function function is given by:
where is the Pochhammer symbol (see
pochhammer
).
If , this sum converges.
Otherwise there is an error.
The eps
argument gives the required precision for its computation.
It is the attr(, "epsilon")
attribute of the returned value.
Sometimes, the convergence is too slow and the required precision cannot be reached.
If this happens, the attr(, "epsilon")
attribute is the precision that was really reached.
Value
A numeric value: the value of the Lauricella function,
with two attributes attr(, "epsilon")
(precision of the result) and attr(, "k")
(number of iterations).
Author(s)
Pierre Santagostini, Nizar Bouhlel
References
N. Bouhlel, A. Dziri, Kullback-Leibler Divergence Between Multivariate Generalized Gaussian Distributions. IEEE Signal Processing Letters, vol. 26 no. 7, July 2019. doi:10.1109/LSP.2019.2915000