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#' Create a Tukey distribution
#'
#' Tukey's studentized range distribution, used for Tukey's
#' honestly significant differences test in ANOVA.
#'
#' @param nmeans Sample size for each range.
#' @param df Degrees of freedom.
#' @param nranges Number of groups being compared.
#'
#' @return A `Tukey` object.
#' @export
#'
#' @family continuous distributions
#'
#' @details
#'
#' We recommend reading this documentation on
#' <https://alexpghayes.github.io/distributions3/>, where the math
#' will render with additional detail and much greater clarity.
#'
#' **Support**: \eqn{R^+}, the set of positive real numbers.
#'
#' Other properties of Tukey's Studentized Range Distribution
#' are omitted, largely because the distribution is not fun
#' to work with.
#'
#' @examples
#'
#' set.seed(27)
#'
#' X <- Tukey(4L, 16L, 2L)
#' X
#'
#' cdf(X, 4)
#' quantile(X, 0.7)
Tukey <- function(nmeans, df, nranges) {
stopifnot(
"parameter lengths do not match (only scalars are allowed to be recycled)" =
length(nmeans) == length(df) & length(nmeans) == length(nranges) |
sum(c(length(nmeans) == 1, length(df) == 1, length(nranges) == 1)) >= 2 |
length(nmeans) == length(df) & length(nranges) == 1 |
length(nmeans) == length(nranges) & length(df) == 1 |
length(df) == length(nranges) & length(nmeans) == 1
)
d <- data.frame(nmeans = nmeans, df = df, nranges = nranges)
class(d) <- c("Tukey", "distribution")
d
}
#' Draw a random sample from a Tukey distribution
#'
#' @inherit Tukey examples
#'
#' @param x A `Tukey` object created by a call to [Tukey()].
#' @param n The number of samples to draw. Defaults to `1L`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Unused. Unevaluated arguments will generate a warning to
#' catch mispellings or other possible errors.
#'
#' @return In case of a single distribution object or `n = 1`, either a numeric
#' vector of length `n` (if `drop = TRUE`, default) or a `matrix` with `n` columns
#' (if `drop = FALSE`).
#' @export
#'
random.Tukey <- function(x, n = 1L, drop = TRUE, ...) {
n <- make_positive_integer(n)
if (n == 0L) return(numeric(0L))
rtukey <- function(n, nmeans, df, nranges = 1) qtukey(runif(n), nmeans = nmeans, df = df, nranges = nranges)
FUN <- function(at, d) rtukey(n = at, nmeans = d$nmeans, df = d$df, nranges = d$nranges)
apply_dpqr(d = x, FUN = FUN, at = n, type = "random", drop = drop)
}
#' Evaluate the cumulative distribution function of a Tukey distribution
#'
#' @inherit Tukey examples
#'
#' @param d A `Tukey` distribution created by a call to [Tukey()].
#' @param x A vector of elements whose cumulative probabilities you would
#' like to determine given the distribution `d`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{d} be evaluated
#' at all elements of \code{x} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{d} and \code{x} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{ptukey}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family Tukey distribution
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(x)` columns (if `drop = FALSE`). In case of a vectorized distribution
#' object, a matrix with `length(x)` columns containing all possible combinations.
#' @export
#'
cdf.Tukey <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) ptukey(q = at, nmeans = d$nmeans, df = d$df, nranges = d$nranges, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "probability", drop = drop, elementwise = elementwise)
}
#' Determine quantiles of a Tukey distribution
#'
#' @inherit Tukey examples
#' @inheritParams cdf.Tukey
#'
#' @param probs A vector of probabilities.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{x} be evaluated
#' at all elements of \code{probs} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{x} and \code{probs} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{qtukey}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(probs)` columns (if `drop = FALSE`). In case of a vectorized
#' distribution object, a matrix with `length(probs)` columns containing all
#' possible combinations.
#' @export
#'
#' @family Tukey distribution
#'
quantile.Tukey <- function(x, probs, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) qtukey(p = at, nmeans = x$nmeans, df = x$df, nranges = x$nranges, ...)
apply_dpqr(d = x, FUN = FUN, at = probs, type = "quantile", drop = drop, elementwise = elementwise)
}
#' Return the support of the Tukey distribution
#'
#' @param d An `Tukey` object created by a call to [Tukey()].
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Currently not used.
#'
#' @return A vector of length 2 with the minimum and maximum value of the support.
#'
#' @export
support.Tukey <- function(d, drop = TRUE, ...) {
ellipsis::check_dots_used()
min <- rep(0, length(d))
max <- rep(Inf, length(d))
make_support(min, max, d, drop = drop)
}
#' @exportS3Method
is_discrete.Tukey <- function(d, ...) {
ellipsis::check_dots_used()
setNames(rep.int(FALSE, length(d)), names(d))
}
#' @exportS3Method
is_continuous.Tukey <- function(d, ...) {
ellipsis::check_dots_used()
setNames(rep.int(TRUE, length(d)), names(d))
}
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