# Approximating ratio of incomplete gamma functions

Discussion in 'Scientific Statistics Math' started by Paul, Dec 15, 2011.

1. ### PaulGuest

Thanks to Mathematica, I have an expression for the mean of a right-
truncated inverse chi-square distribution:

Btrunc = TruncatedDistribution[{0, W/(B*(D - 1))},
InverseChiSquareDistribution[D - 1]]; Mean[Btrunc]

The expression is a ratio of two incomplete gamma functions --

Gamma[1/2 (-3 + D), (B (-1 + D))/(
2 W)]/(2 Gamma[1/2 (-1 + D), (B (-1 + D))/(2 W)])

-- which is fine as long I stay in Mathematica. However, I will need
to deploy this result in a statistics package, and two problems will
arise:

(1) Some statistics packages, such as SAS, have not implemented the
incomplete gamma function.
(2) Many programming languages are going to have trouble calculating
the ratio of two very large numbers, which this is.

So I wonder whether there's a simpler way to approximate the result.
It may help that D is an integer of at least 5, and that W and B are
positive. Many thanks for any suggestions.

Best,
Paul

Paul, Dec 15, 2011

2. ### RGuest

Paul,

Have you investigated the NLMIXED procedure in SAS which allows you to