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#' Inverse Weibull distribution maximum likelihood estimation
#'
#' The maximum likelihood estimate of `shape` and `rate` are calculated
#' by calling [`mlweibull`][mlweibull] on the transformed data.
#'
#' For the density function of the log normal distribution see
#' [InverseWeibull][actuar::InverseWeibull].
#'
#' @param x a (non-empty) numeric vector of data values.
#' @param na.rm logical. Should missing values be removed?
#' @param ... passed to [`mlweibull`][mlweibull].
#' @return `mlinvweibull` returns an object of [class][base::class]
#' `univariateML`. This is a named numeric vector with maximum likelihood
#' estimates for `shape` and `rate` 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
#' mlinvweibull(precip)
#' @seealso [InverseWeibull][actuar::InverseWeibull] for the Inverse Weibull
#' density.
#' @references Kleiber, C. and Kotz, S. (2003), Statistical Size Distributions
#' in Economics and Actuarial Sciences, Wiley.
#'
#' Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models,
#' From Data to Decisions, Fourth Edition, Wiley.
#'
#' Dutang, C., Goulet, V., & Pigeon, M. (2008). actuar: An R package for
#' actuarial science. Journal of Statistical Software, 25(7), 1-37.
#' @export
mlinvweibull <- 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)
y <- 1 / x
n <- length(x)
object <- mlweibull(y, ...)
names(object) <- c("shape", "rate")
shape <- object[1]
scale <- 1 / object[2]
G <- mean(log(x))
Ma <- mean(x^-shape)
class(object) <- "univariateML"
attr(object, "model") <- "InverseWeibull"
attr(object, "density") <- "actuar::dinvweibull"
attr(object, "logLik") <- unname(n * (log(shape) + shape * (log(scale) - G) -
scale^shape * Ma - G))
attr(object, "support") <- c(0, Inf)
attr(object, "call") <- match.call()
object
}
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