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Topic: Approximating ratio of incomplete gamma functions
Replies: 1   Last Post: Dec 15, 2011 9:24 PM

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R

Posts: 31
Registered: 10/8/10
Re: Approximating ratio of incomplete gamma functions
Posted: Dec 15, 2011 9:24 PM
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On Dec 15, 8:31 am, Paul <paulvonhip...@yahoo.com> wrote:
> 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,

Have you investigated the NLMIXED procedure in SAS which allows you to
write your own likelihood function?

Ryan



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