R/mlweibull.R

Defines functions mlweibull

Documented in mlweibull

#' Weibull distribution maximum likelihood estimation
#'
#' Uses Newton-Raphson to estimate the parameters of the Weibull distribution.
#'
#' For the density function of the Weibull distribution see
#'    [Weibull][stats::Weibull].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... `shape0` is an optional starting value for the `shape` parameter.
#'     `rel.tol` is the relative accuracy requested, defaults
#'     to `.Machine$double.eps^0.25`. `iterlim` is a positive integer
#'     specifying the maximum number of iterations to be performed before the
#'     program is terminated (defaults to `100`).
#'
#' @return `mlweibull` returns an object of [class][base::class] `univariateML`.
#'    This is a named numeric vector with maximum likelihood estimates for
#'    `shape` 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`}
#' @seealso [Weibull][stats::Weibull] for the Weibull density.
#' @examples
#' BIC(mlweibull(precip))
#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous
#' Univariate Distributions, Volume 1, Chapter 21. Wiley, New York.
#' @export

mlweibull <- 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)

  dots <- list(...)

  shape0 <- if (!is.null(dots$sigma0)) dots$shape0 else 1

  rel.tol <- if (!is.null(dots$rel.tol)) {
    dots$rel.tol
  } else {
    .Machine$double.eps^0.25
  }

  iterlim <- if (!is.null(dots$iterlim)) dots$iterlim else 100

  log_x <- log(x)
  l_hat <- mean(log_x)
  log_xsq <- log_x^2

  for (i in 1:iterlim) {
    shape0_lsum <- mean(x^shape0 * log_x)
    shape0_lsum_sqr <- mean(x^shape0 * log_xsq)
    shape0_sum <- mean(x^shape0)
    A <- shape0_lsum / shape0_sum
    B <- shape0_lsum_sqr / shape0_sum
    top <- 1 / shape0 + l_hat - A
    bottom <- -1 / shape0^2 + A^2 - B
    shape <- shape0 - top / bottom

    if (abs((shape0 - shape) / shape0) < rel.tol) break

    shape0 <- shape
  }

  if (i == iterlim) {
    warning(paste0(
      "The iteration limit (iterlim = ", iterlim, ") was reached",
      " before the relative tolerance requirement (rel.tol = ",
      rel.tol, ")."
    ))
  }

  ## Given the shape, the scale is easy to compute.
  scale <- (mean(x^shape))^(1 / shape)
  shape_sum <- mean(x^shape)
  n <- length(x)
  object <- c(shape = shape, scale = scale)
  class(object) <- "univariateML"
  attr(object, "model") <- "Weibull"
  attr(object, "density") <- "stats::dweibull"
  attr(object, "logLik") <- n * (log(shape) - log(scale) +
    (shape - 1) * (l_hat - log(scale)) - scale^-shape * shape_sum)
  attr(object, "support") <- c(0, Inf)
  attr(object, "n") <- length(x)
  attr(object, "call") <- match.call()
  object
}

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univariateML documentation built on Jan. 25, 2022, 5:09 p.m.