TransformedDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg121145] TransformedDistribution
- From: paulvonhippel at yahoo <paulvonhippel at yahoo.com>
- Date: Wed, 31 Aug 2011 06:05:13 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
I am seeking the mean of a variable which includes the weighted sum of
two chi-square variables. When I ask the question the obvious way
(below), Mathematica takes a long time to return an unwieldy answer
that is undefined for most values of n1 & n2. I'd be grateful if
someone could suggest a more tractable way to pose the problem.
Here's a simplified version of the problem:
Mean[
TransformedDistribution[
Sqrt[\[FormalX]2 n2 + \[FormalX]1 n1 ], {\[FormalX]1 \[Distributed]
ChiSquareDistribution[n1], \[FormalX]2 \[Distributed]
ChiDistribution[n2]}]]
And whatI really want to do is a little more complicated:
TransformedDistribution[\[FormalX]2 Sqrt[((\[FormalX]3 +
den) n + \[FormalX]1 Subscript[n, obs])/(
den (-1 + n) n)] \[Sigma], {\[FormalX]1 \[Distributed]
ChiSquareDistribution[1], \[FormalX]2 \[Distributed]
ChiDistribution[-1 + Subscript[n,
obs]], \[FormalX]3 \[Distributed]
ChiSquareDistribution[-1 + Subscript[n, mis]]}]