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Author Comment/Response
Peter Pein
05/21/13 4:12pm

Hi,

even if I define:

mu = {4, 5};
stdev = {3, 2};

With[{sq = Sqrt[(1 + E) (1 + E^2) (1 + E + E^2) (1 + E^3 + E^6)]},
correlationMatrix = {{1, v}, {v, 1}} /.
v -> 1/6 Log[1/2 (2 + (E - 1) sq)]
];

covarianceMatrix =
DiagonalMatrix[stdev].correlationMatrix.DiagonalMatrix[stdev];

dist = LogMultinormalDistribution[mu, covarianceMatrix];

and
Correlation[dist] // Simplify

gives {{1, 1/2}, {1/2, 1}},

then

SeedRandom[123];
tbl = ParallelTable[
Correlation[RandomVariate[dist, 10^4]][[1, 2]], {i, 10^4}];

has got the mean value 0.806835.

It seems, I misunderstood something too :( but at least the correlation of the distribution is OK :-\

Peter

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Subject (listing for 'False covariance')
Author Date Posted
False covariance J. Karrey 05/13/13 06:44am
Re: False covariance Peter Pein 05/21/13 2:21pm
Re: False covariance Peter Pein 05/21/13 4:12pm
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