Logit-Normal distribution maximum likelihood estimation

The maximum likelihood estimate of mu is the empirical mean of the logit transformed data and the maximum likelihood estimate of sigma is the square root of the logit transformed biased sample variance.

Usage

mllogitnorm(x, na.rm = FALSE, ...)

Arguments

x: a (non-empty) numeric vector of data values.
na.rm: logical. Should missing values be removed?
...: currently affects nothing.

Value

mllogitnorm returns an object of class

univariateML. This is a named numeric vector with maximum likelihood estimates for mu and sigma and the following attributes:

model: The name of the model.
density: The density associated with the estimates.
logLik: The loglikelihood at the maximum.
support: The support of the density.
n: The number of observations.
call: The call as captured my match.call

Details

For the density function of the logit-normal distribution see dlogitnorm.

References

Atchison, J., & Shen, S. M. (1980). Logistic-normal distributions: Some properties and uses. Biometrika, 67(2), 261-272.

Examples

AIC(mllogitnorm(USArrests$Rape / 100))
#> [1] -99.95017