R/mlbetapr.R

In JonasMoss/univariateML: Maximum Likelihood Estimation for Univariate Densities

#' Beta prime distribution maximum likelihood estimation
#'
#' This function does not estimate the scale parameter for the `BetaPrime`
#'     distribution. Transforms the data and uses `stat::nlm` to estimate
#'     the parameters of the Beta distribution.
#'
#' For the density function of the Beta prime distribution see
#'     [BetaPrime][extraDistr::BetaPrime].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... passed to [`mlbeta`][mlbeta].
#' @return `mlbetapr` returns an object of [class][base::class] `univariateML`.
#'    This is a named numeric vector with maximum likelihood estimates for
#'    `shape1` and `shape2` 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`}
#' @details For `type`, the option `none` is fastest.
#' @seealso [BetaPrime][extraDistr::BetaPrime] for the Beta prime density,
#'   [nlm][stats::nlm] for the optimizer this function uses, [mlbeta] for
#'   the Beta distribution maximum likelihood estimator.
#' @examples
#' AIC(mlbetapr(USArrests$Rape))
#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
#' Continuous Univariate Distributions, Volume 2, Chapter 25. Wiley, New York.
#' @export
mlbetapr <- function(x, na.rm = FALSE, ...) {}

univariateML_metadata$mlbetapr <- list(
  "model" = "BetaPrime",
  "density" = "extraDistr::dbetapr",
  "support" = intervals::Intervals(c(0, Inf), closed = c(TRUE, FALSE)),
  "names" = c("shape1", "shape2"),
  "default" = c(2, 3)
)

mlbetapr_ <- function(x, ...) {
  estimates <- mlbeta(x / (x + 1), na.rm = FALSE, ...)
  alpha <- estimates[1]
  beta <- estimates[2]
  logLik <- unname(-length(x) * (lbeta(alpha, beta) -
    (alpha - 1) * mean(log(x)) +
    (alpha + beta) * mean(log(1 + x))))
  list(estimates = estimates, logLik = logLik)
}