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