Bug in PDF[MultinormalDistribution[..],..]
- To: mathgroup at smc.vnet.net
- Subject: [mg54735] Bug in PDF[MultinormalDistribution[..],..]
- From: Mark Fisher <mark at markfisher.net>
- Date: Mon, 28 Feb 2005 03:27:37 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
There appears to be a bug in PDF[MultinormalDistribution[..],..]. In
what follows, sigma is a valid covariance matrix as long as b is not 0.
However, negative b produces a negative value for the PDF, which is
incorrect.
Clear[b,f,sigma]
sigma = {{2b^2, b}, {b, 1}}
Det[sigma] == b^2
f[b_] = PDF[MultinormalDistribution[{0, 0}, sigma], {0, 0}]
f[-1] < 0
I believe the source of the error is an inapropriate PowerExpand in line
707 of MultinormalDistribution.m in the Statistics directory.
I am using version 5.1 for Windows.
BTW, after poking around in MultinormalDistribution.m, I discovered that
MultinormalDistribution[{0,0}, sigma] acquires a third (hidden) part
where the CholeskyDecomposition of sigma is stored:
mvn = MultinormalDistribution[{0,0}, sigma];
Simplify[mvn[[3]].Transpose[mvn[[3]]] == mvn[[2]], b \[Element] Reals]
--Mark