Efficient Computation involving a Hypergeometric function...
- To: mathgroup at smc.vnet.net
- Subject: [mg72584] Efficient Computation involving a Hypergeometric function...
- From: "Richard Palmer" <rhpalmer at gmail.com>
- Date: Wed, 10 Jan 2007 03:23:08 -0500 (EST)
I have a discrete distribution:
\!\(f\ \ = \ \ Binomial[x + n, x]\ p\^\(x + 1\)\ \((1 - p)\)\^n\)
Here p and x are fixed, p is real between 0 and 1, x and n are
integers greater than or equal to zero, and n is the parameter
(n,0,Infinity).
The CDF is
\!\(1 - \(\((1 -
p)\)\^\(1 + n\)\ p\^\(1 + x\)\ Ã[2 + n + x]\ \
Hypergeometric2F1Regularized[1, 2 + n + x, 2 + n, 1 - p]\)\/Ã[1 + x]\)
where n is actually Floor[n].
Does anybody see a simplification or asymtotic for the CDF that
provides an efficient way to compute this for large n (say n ge
1000)? I need to solve CDF==k for various fixed p and x.
Thanks in advance!
--
Richard Palmer