Last data update: 2014.03.03
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R: Expectation of a product of powers of Normal or T random...
Expectation of a product of powers of Normal or T random
variables
Description
Compute the mean of prod(x)^power when x follows T_dof(mu,sigma)
distribution (dof= -1 for multivariate Normal).
Usage
eprod(m, S, power = 1, dof = -1)
Arguments
m |
Location parameter
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S |
Scale matrix. For multivariate T with dof>2 the covariance is
S*dof/(dof-2). For the multivariate Normal the covariance is S.
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power |
Power that the product is raised to
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dof |
Degrees of freedom of the multivariate T. Set to -1 for the
multivariate Normal.
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Details
The calculation is based on the computationally efficient approach by Kan (2008).
Value
Expectation of the above-mentioned product
Author(s)
John Cook
References
Kan R. From moments of sum to moments of product. Journal of
Multivariate Analysis 99 (2008), 542-554.
Examples
#Check easy independence case
m <- c(0,3); S <- matrix(c(2,0,0,1),ncol=2)
eprod(m, S, power=2)
(m[1]^2+S[1][1])*(m[2]^2+S[2][2])
Results
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