# twCoefLogitnormE: twCoefLogitnormE In logitnorm: Functions for the Logitnormal Distribution

## Description

Estimating coefficients of logitnormal distribution from expected value, i.e. mean, and upper quantile.

## Usage

 ```1 2 3``` ```twCoefLogitnormE(mean, quant, perc = c(0.975), method = "BFGS", theta0 = c(mu = 0, sigma = 1), returnDetails = FALSE, ...) ```

## Arguments

 `mean` the expected value of the density function `quant` the quantile values `perc` the probabilities for which the quantiles were specified `method` method of optimization (see `optim`) `theta0` starting parameters `returnDetails` if TRUE, the full output of optim is returned with attribute resOptim `...`

## Value

named numeric matrix with estimated parameters of the logitnormal distribution. colnames: `c("mu","sigma")`

## Author(s)

Thomas Wutzler

`logitnorm`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```# estimate the parameters (thetaE <- twCoefLogitnormE(0.7,0.9)) x <- seq(0,1,length.out = 41)[-c(1,41)] # plotting grid px <- plogitnorm(x,mu = thetaE[1],sigma = thetaE[2]) #percentiles function plot(px~x); abline(v = c(0.7,0.9),col = "gray"); abline(h = c(0.5,0.975),col = "gray") dx <- dlogitnorm(x,mu = thetaE[1],sigma = thetaE[2]) #density function plot(dx~x); abline(v = c(0.7,0.9),col = "gray") z <- rlogitnorm(1e5, mu = thetaE[1],sigma = thetaE[2]) mean(z) # about 0.7 # vectorized (theta <- twCoefLogitnormE(mean = seq(0.4,0.8,by = 0.1),quant = 0.9)) ```