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#' The Uniform distribution
#'
#' @description
#' `r lifecycle::badge('stable')`
#'
#' A distribution with constant density on an interval.
#'
#' @inheritParams stats::dunif
#'
#' @details
#'
#' We recommend reading this documentation on
#' <https://pkg.mitchelloharawild.com/distributional/>, where the math
#' will render nicely.
#'
#' In the following, let \eqn{X} be a Poisson random variable with parameter
#' `lambda` = \eqn{\lambda}.
#'
#' **Support**: \eqn{[a,b]}{[a,b]}
#'
#' **Mean**: \eqn{\frac{1}{2}(a+b)}
#'
#' **Variance**: \eqn{\frac{1}{12}(b-a)^2}
#'
#' **Probability mass function (p.m.f)**:
#'
#' \deqn{
#' f(x) = \frac{1}{b-a} for x \in [a,b]
#' }{
#' f(x) = \frac{1}{b-a} for x in [a,b]
#' }
#' \deqn{
#' f(x) = 0 otherwise
#' }{
#' f(x) = 0 otherwise
#' }
#'
#' **Cumulative distribution function (c.d.f)**:
#'
#' \deqn{
#' F(x) = 0 for x < a
#' }{
#' F(x) = 0 for x < a
#' }
#' \deqn{
#' F(x) = \frac{x - a}{b-a} for x \in [a,b]
#' }{
#' F(x) = \frac{x - a}{b-a} for x in [a,b]
#' }
#' \deqn{
#' F(x) = 1 for x > b
#' }{
#' F(x) = 1 for x > b
#' }
#'
#' **Moment generating function (m.g.f)**:
#'
#' \deqn{
#' E(e^{tX}) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0
#' }{
#' E(e^(tX)) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0
#' }
#' \deqn{
#' E(e^{tX}) = 1 for t = 0
#' }{
#' E(e^(tX)) = 1 for t = 0
#' }
#'
#' @seealso [stats::Uniform]
#'
#' @examples
#' dist <- dist_uniform(min = c(3, -2), max = c(5, 4))
#'
#' dist
#' mean(dist)
#' variance(dist)
#' skewness(dist)
#' kurtosis(dist)
#'
#' generate(dist, 10)
#'
#' density(dist, 2)
#' density(dist, 2, log = TRUE)
#'
#' cdf(dist, 4)
#'
#' quantile(dist, 0.7)
#'
#' @name dist_uniform
#' @export
dist_uniform <- function(min, max){
min <- vec_cast(min, double())
max <- vec_cast(max, double())
if(any(min > max)){
abort("The min of a Uniform distribution must be less than max.")
}
new_dist(l = min, u = max, class = "dist_uniform")
}
#' @export
format.dist_uniform <- function(x, digits = 2, ...){
sprintf(
"U(%s, %s)",
format(x[["l"]], digits = digits, ...),
format(x[["u"]], digits = digits, ...)
)
}
#' @export
density.dist_uniform <- function(x, at, ...){
stats::dunif(at, x[["l"]], x[["u"]])
}
#' @export
log_density.dist_uniform <- function(x, at, ...){
stats::dunif(at, x[["l"]], x[["u"]], log = TRUE)
}
#' @export
quantile.dist_uniform <- function(x, p, ...){
stats::qunif(p, x[["l"]], x[["u"]])
}
#' @export
cdf.dist_uniform <- function(x, q, ...){
stats::punif(q, x[["l"]], x[["u"]])
}
#' @export
generate.dist_uniform <- function(x, times, ...){
stats::runif(times, x[["l"]], x[["u"]])
}
#' @export
mean.dist_uniform <- function(x, ...){
(x[["u"]]+x[["l"]])/2
}
#' @export
covariance.dist_uniform <- function(x, ...){
(x[["u"]]-x[["l"]])^2/12
}
#' @export
skewness.dist_uniform <- function(x, ...) 0
#' @export
kurtosis.dist_uniform <- function(x, ...) -6/5
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