# logitNormMean: Calculate the mean of a distribution whose logit is Gaussian In martinbryan/SUMMER: Small-Area-Estimation Unit/Area Models and Methods for Estimation in R

 logitNormMean R Documentation

## Calculate the mean of a distribution whose logit is Gaussian

### Description

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

### 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.

### Value

A vector of expectations of the specified random variables

John Paige

### Examples

mus = c(-5, 0, 5)
sigmas = rep(1, 3)
logitNormMean(cbind(mus, sigmas))
logitNormMean(cbind(mus, sigmas), TRUE)



martinbryan/SUMMER documentation built on April 10, 2024, 5:03 a.m.