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#' Logistic distribution maximum likelihood estimation
#'
#' Calculates the estimates using `nlm` with an exponential transform of the
#' location parameter.
#'
#' For the density function of the logistic distribution see
#' [Logistic][stats::Logistic].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... currently affects nothing.
#' @return `mllogis` returns an object of [class][base::class] `univariateML`.
#' This is a named numeric vector with maximum likelihood estimates for
#' `location` and `scale` 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
#' mllogis(precip)
#' @seealso [Logistic][stats::Logistic] for the Logistic density,
#' [nlm][stats::nlm] for the optimizer this function uses.
#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
#' Continuous Univariate Distributions, Volume 2, Chapter 23. Wiley, New York.
#' @export
mllogis <- function(x, na.rm = FALSE, ...) {
if (na.rm) x <- x[!is.na(x)] else assertthat::assert_that(!anyNA(x))
ml_input_checker(x)
m <- stats::median(x)
mad <- stats::median(abs(x - m))
start <- c(m, log(mad))
f <- function(p) -sum(stats::dlogis(x, p[1], exp(p[2]), log = TRUE))
values <- suppressWarnings(stats::nlm(
f = f,
p = start
))
object <- c(
location = values$estimate[1],
scale = exp(values$estimate[2])
)
class(object) <- "univariateML"
attr(object, "model") <- "Logistic"
attr(object, "density") <- "stats::dlogis"
attr(object, "logLik") <- -values$minimum
attr(object, "support") <- c(-Inf, Inf)
attr(object, "n") <- length(x)
attr(object, "call") <- match.call()
object
}
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