Calculate the mean of a distribution whose logit is Gaussian

Adapted from logitnorm package. Calculates the mean of a distribution whose logit is Gaussian. Each row of muSigmaMat is a mean and standard deviation on the logit scale.

Usage

logitNormMean(muSigmaMat, logisticApprox = FALSE, ...)

Arguments

muSigmaMat

An n x 2 matrix where each row is \(\mu\) and \(\sigma\) on the logit scale for an independent random variable.

logisticApprox

Whether or not to use logistic approximation to speed up computation. See details for more information.

...

More arguments, passed to integrate function

Value

A vector of expectations of the specified random variables

Details

If \(\mbox{logit}(Y) \sim N(\mu, \sigma^2)\), This function calculates \(E[Y]\) via either numerical integration or by assuming that Y follows a logistic distribution. Under this approximation, setting \(k = 16 \sqrt(3) / (15 \pi)\), we approximate the expectation as: $$E[Y] = expit(\mu / \sqrt(1 + k^2 \sigma^2))$$. The above logistic approximation speeds up the computation, but also sacrifices some accuracy.

Author

John Paige

Examples

mus = c(-5, 0, 5)
sigmas = rep(1, 3)
logitNormMean(cbind(mus, sigmas))
#> [1] 0.01079679 0.50000000 0.98920321
logitNormMean(cbind(mus, sigmas), TRUE)
#> [1] 0.01325606 0.50000000 0.98674394