Exact mean and covariance formulas after diagonal transformations of a multivariate normal
Abstract
Consider X N( 0, ) and Y = (f1(X1), f2(X2),…, fd(Xd)). We call this a diagonal transformation of a multivariate normal. In this paper we compute exactly the mean vector and covariance matrix of the random vector Y. This is done two different ways: One approach uses a series expansion for the function fi and the other a transform method. We compute several examples, show how the covariance entries can be estimated, and compare the theoretical results with numerical ones.
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