Multivariate Normal Integration
Given a covariance matrix, a means vector, and vectors of lower and upper bounds, returns the multivariate normal integral across the space between bounds.
omxMnor(covariance, means, lbound, ubound)
covariance |
the covariance matrix describing the multivariate normal distribution. |
means |
a row vector containing means of the variables of the underlying distribution. |
lbound |
a row vector containing the lower bounds of the integration in each variable. |
ubound |
a row vector containing the upper bounds of the integration in each variable. |
The order of columns in the ‘means’, ‘lbound’, and ‘ubound’ vectors are assumed to be the same as that of the covariance matrix. That is, means[i] is considered to be the mean of the variable whose variance is in covariance[i,i]. That variable will be integrated from lbound[i] to ubound[i] as part of the integration.
The value of ubound[i] or lbound[i] may be set to Inf or -Inf if a boundary at positive or negative infinity is desired.
For all i, ubound[i] must be strictly greater than lbound[i].
data(myFADataRaw) covariance <- cov(myFADataRaw[,1:3]) means <- colMeans(myFADataRaw[,1:3]) lbound <- c(-Inf, 0, 1) # Integrate from -Infinity to 0 on first variable ubound <- c(0, Inf, 2.5) # From 0 to +Infinity on second, and from 1 to 2.5 on third omxMnor(covariance, means, lbound, ubound) # 0.0005995 # An alternative specification of the bounds follows # Integrate from -Infinity to 0 on first variable v1bound = c(-Inf, 0) # From 0 to +Infinity on second v2bound = c(0, Inf) # and from 1 to 2.5 on third v3bound = c(1, 2.5) bounds <- cbind(v1bound, v2bound, v3bound) lbound <- bounds[1,] ubound <- bounds[2,] omxMnor(covariance, means, lbound, ubound)
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