Approximating ratio of incomplete gamma functions
- To: mathgroup at smc.vnet.net
- Subject: [mg123691] Approximating ratio of incomplete gamma functions
- From: paul <paulvonhippel at yahoo.com>
- Date: Fri, 16 Dec 2011 05:41:20 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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, which is
usable within 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.
I imagine Mathematica has tools for developing approximations, but I
am not familiar with them. Many thanks for any suggestions.
Best,
Paul