R/mllogitnorm.R

In univariateML: Maximum Likelihood Estimation for Univariate Densities

#' 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.
#'
#' For the density function of the logit-normal distribution see
#'    [dlogitnorm][logitnorm::dlogitnorm].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... currently affects nothing.
#' @return `mllogitnorm` returns an object of [class][base::class]
#'    `univariateML`. This is a named numeric vector with maximum likelihood
#'    estimates for `mu` and `sigma` and the following attributes:
#'     \item{`model`}{The name of the model.}
#'     \item{`density`}{The density associated with the estimates.}
#'     \item{`logLik`}{The loglikelihood at the maximum.}
#'     \item{`support`}{The support of the density.}
#'     \item{`n`}{The number of observations.}
#'     \item{`call`}{The call as captured my `match.call`}
#' @examples
#' AIC(mllogitnorm(USArrests$Rape / 100))
#' @seealso [Normal][stats::dnorm] for the normal density.
#' @references Atchison, J., & Shen, S. M. (1980). Logistic-normal
#' distributions: Some properties and uses. Biometrika, 67(2), 261-272.
#' @export
mllogitnorm <- function(x, na.rm = FALSE, ...) {}

univariateML_metadata$mllogitnorm <- list(
  "model" = "LogitNormal",
  "density" = "logitnorm::dlogitnorm",
  "support" = intervals::Intervals(c(0, 1), closed = c(FALSE, FALSE)),
  "names" = c("mu", "sigma"),
  "default" = c(2, 3)
)

mllogitnorm_ <- function(x, ...) {
  n <- length(x)
  y <- stats::qlogis(x)
  mu <- mean(y)
  sigma <- sqrt(stats::var(y) * (n - 1) / n)

  H <- mean(log(x))
  G <- mean(log(1 - x))

  estimates <- c(mu = mu, sigma = sigma)
  logLik <-
    -n / 2 * (1 + log(2 * pi) + 2 * log(sigma) + 2 * H + 2 * G)
  list(estimates = estimates, logLik = logLik)
}