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

## Description

Estimating coefficients of logitnormal distribution from a vector of quantiles and perentiles (non-vectorized).

## Usage

 ```1 2 3 4 5 6 7``` ```twCoefLogitnormN(quant, perc = c(0.5, 0.975), method = "BFGS", theta0 = c(mu = 0, sigma = 1), returnDetails = FALSE, ...) ```

## Arguments

 `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 instead of only entry par `...` further parameters passed to optim, e.g. control=list(maxit=1000)

## Value

named numeric vector with estimated parameters of the logitnormal distrubtion.

names: `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``` ``` # experiment of re-estimation the parameters from generated observations thetaTrue <- c(mu=0.8, sigma=0.7) obsTrue <- rlogitnorm(thetaTrue["mu"],thetaTrue["sigma"], n=500) obs <- obsTrue + rnorm(100, sd=0.05) # some observation uncertainty plot(density(obsTrue),col="blue"); lines(density(obs)) # re-estimate parameters based on the quantiles of the observations (theta <- twCoefLogitnorm( median(obs), quantile(obs,probs=0.9), perc = 0.9)) # add line of estimated distribution x <- seq(0,1,length.out=41)[-c(1,41)] # plotting grid dx <- dlogitnorm(x,mu=theta[1],sigma=theta[2]) lines( dx ~ x, col="orange") ```