R/mlpareto.R

In JonasMoss/univariateML: Maximum Likelihood Estimation for Univariate Densities

#' Pareto distribution maximum likelihood estimation
#'
#' The maximum likelihood estimate of `b` is the minimum of `x` and the
#'     maximum likelihood estimate of `a` is
#'     `1/(mean(log(x)) - log(b))`.
#'
#' For the density function of the Pareto distribution see
#'    [Pareto][extraDistr::Pareto].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... currently affects nothing.
#' @return `mlpareto` returns an object of [class][base::class] `univariateML`.
#'    This is a named numeric vector with maximum likelihood estimates for
#'    `a` and `b` 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
#' mlpareto(precip)
#' @seealso [Pareto][extraDistr::Pareto] for the Pareto density.
#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous
#' Univariate Distributions, Volume 1, Chapter 20. Wiley, New York.
#' @export
mlpareto <- function(x, na.rm = FALSE, ...) {}

univariateML_metadata$mlpareto <- list(
  "model" = "Pareto",
  "density" = "extraDistr::dpareto",
  "support" = stats::setNames(intervals::Intervals(c(0, Inf), closed = c(TRUE, FALSE)), c("a", "Inf")),
  "names" = c("a", "b"),
  "default" = c(1, 2)
)

mlpareto_ <- function(x, ...) {
  m <- mean(log(x))
  b <- min(x)
  a <- 1 / (m - log(b))

  estimates <- c(a, b)
  logLik <- length(x) * (log(a) + a * log(b) - (a + 1) * m)
  list(estimates = estimates, logLik = logLik)
}