R/mlinvgauss.R

In univariateML: Maximum Likelihood Estimation for Univariate Densities

#' Inverse Gaussian (Wald) maximum likelihood estimation
#'
#' The maximum likelihood estimate of `mean` is the empirical mean and the
#'     maximum likelihood estimate of `1/shape` is the difference between
#'     the mean of reciprocals and the reciprocal of the mean.
#'
#' For the density function of the Inverse Gamma distribution see
#'     [InverseGaussian][actuar::InverseGaussian].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... currently affects nothing.
#' @return `mlinvgauss` returns an object of [class][base::class]
#'    `univariateML`. This is a named numeric vector with maximum likelihood
#'    estimates for `mean` and `shape` 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
#' mlinvgauss(precip)
#' @seealso [InverseGaussian][actuar::InverseGaussian] for the
#' Inverse Gaussian density.
#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
#' Continuous Univariate Distributions, Volume 1, Chapter 15. Wiley, New York.
#' @export

mlinvgauss <- function(x, na.rm = FALSE, ...) {
  if (na.rm) x <- x[!is.na(x)] else assertthat::assert_that(!anyNA(x))
  ml_input_checker(x)
  assertthat::assert_that(min(x) > 0)
  n <- length(x)

  mu <- mean(x)
  lambda <- 1 / (mean(1 / x) - 1 / mu)
  object <- c(mean = mu, shape = lambda)
  L <- mean(log(x))
  S <- mean((x - mean(x))^2 / x)

  class(object) <- "univariateML"
  attr(object, "model") <- "Inverse Gaussian"
  attr(object, "density") <- "actuar::dinvgauss"
  attr(object, "logLik") <-
    -n / 2 * (3 * L - log(lambda) + log(2 * pi) + lambda / mu^2 * S)
  attr(object, "support") <- c(0, Inf)
  attr(object, "n") <- length(x)
  attr(object, "call") <- match.call()
  object
}