# 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 4 5 6 7``` ```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 probabilites 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 attribut resOptim `...`

## Value

named numeric matrix with estimated parameters of the logitnormal distrubtion.

colnames: `c("mu","sigma")`

## Author(s)

Thomas Wutzler

`logitnorm`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40``` ```# 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)) ```