Nothing
#' Create a HyperGeometric distribution
#'
#' To understand the HyperGeometric distribution, consider a set of
#' \eqn{r} objects, of which \eqn{m} are of the type I and
#' \eqn{n} are of the type II. A sample with size \eqn{k} (\eqn{k<r})
#' with no replacement is randomly chosen. The number of observed
#' type I elements observed in this sample is set to be our random
#' variable \eqn{X}. For example, consider that in a set of 20
#' car parts, there are 4 that are defective (type I).
#' If we take a sample of size 5 from those car parts, the
#' probability of finding 2 that are defective will be given by
#' the HyperGeometric distribution (needs double checking).
#'
#'
#' @param m The number of type I elements available.
#' @param n The number of type II elements available.
#' @param k The size of the sample taken.
#'
#' @return A `HyperGeometric` object.
#' @export
#'
#' @family discrete 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.
#'
#' In the following, let \eqn{X} be a HyperGeometric random variable with
#' success probability `p` = \eqn{p = m/(m+n)}.
#'
#' **Support**: \eqn{x \in { \{\max{(0, k-n)}, \dots, \min{(k,m)}}\}}
#'
#' **Mean**: \eqn{\frac{km}{n+m} = kp}
#'
#' **Variance**: \eqn{\frac{km(n)(n+m-k)}{(n+m)^2 (n+m-1)} =
#' kp(1-p)(1 - \frac{k-1}{m+n-1})}
#'
#' **Probability mass function (p.m.f)**:
#'
#' \deqn{
#' P(X = x) = \frac{{m \choose x}{n \choose k-x}}{{m+n \choose k}}
#' }{
#' P(X = x) = \frac{{m \choose x}{n \choose k-x}}{{m+n \choose k}}
#' }
#'
#' **Cumulative distribution function (c.d.f)**:
#'
#' \deqn{
#' P(X \le k) \approx \Phi\Big(\frac{x - kp}{\sqrt{kp(1-p)}}\Big)
#' }
#' **Moment generating function (m.g.f)**:
#'
#' Not useful.
#'
#' @examples
#'
#' set.seed(27)
#'
#' X <- HyperGeometric(4, 5, 8)
#' X
#'
#' random(X, 10)
#'
#' pdf(X, 2)
#' log_pdf(X, 2)
#'
#' cdf(X, 4)
#' quantile(X, 0.7)
HyperGeometric <- function(m, n, k) {
stopifnot(
"parameter lengths do not match (only scalars are allowed to be recycled)" =
length(m) == length(n) & length(m) == length(k) |
sum(c(length(m) == 1, length(n) == 1, length(k) == 1)) >= 2 |
length(m) == length(n) & length(k) == 1 |
length(m) == length(k) & length(n) == 1 |
length(n) == length(k) & length(m) == 1
)
d <- data.frame(m = m, n = n, k = k)
idx <- which(d$k > d$n + d$m)
if (length(idx) == 1) {
stop(
glue::glue(
"k ({d$k[idx]}) cannot be greater than m + n ({d$m[idx]} + {d$n[idx]} = {(d$m+d$n)[idx]})"
)
)
} else if (length(idx) > 1 & length(idx) <= 3) {
stop(
sprintf(
"k {c(%s)} cannot be greater than m + n {c(%s) + c(%s) = c(%s)}",
paste0(d$k[idx], collapse = ", "),
paste0(d$m[idx], collapse = ", "),
paste0(d$n[idx], collapse = ", "),
paste0(d$m[idx] + d$n[idx], collapse = ", ")
)
)
} else if (length(idx) > 3) {
stop(glue::glue("no k is allowed to be greater than m + n"))
}
class(d) <- c("HyperGeometric", "distribution")
d
}
#' @export
mean.HyperGeometric <- function(x, ...) {
ellipsis::check_dots_used()
# Reformulating to match Wikipedia
# N is the population size
N <- x$n + x$m
# K number of success states
K <- x$m
# n number of draws
n <- x$k
rval <- n * K / N
setNames(rval, names(x))
}
#' @export
variance.HyperGeometric <- function(x, ...) {
N <- x$n + x$m
K <- x$m
n <- x$k
rval <- (n * K * (N - K) * (N - n)) / (N^2 * (N - 1))
setNames(rval, names(x))
}
#' @export
skewness.HyperGeometric <- function(x, ...) {
N <- x$n + x$m
K <- x$m
n <- x$k
a <- (N - 2 * K) * (N - 1)^0.5 * (N - 2 * n)
b <- (n * K * (N - K) * (N - n))^0.5 * (N - 2)
rval <- a / b
setNames(rval, names(x))
}
#' @export
kurtosis.HyperGeometric <- function(x, ...) {
N <- x$n + x$m
K <- x$m
n <- x$k
rval <- 1 / (n * K * (N - K) * (N - n) * (N - 2) * (N - 3))
setNames(rval, names(x))
}
#' Draw a random sample from a HyperGeometric distribution
#'
#' Please see the documentation of [HyperGeometric()] for some properties
#' of the HyperGeometric distribution, as well as extensive examples
#' showing to how calculate p-values and confidence intervals.
#'
#' @inherit HyperGeometric examples
#'
#' @param x A `HyperGeometric` object created by a call to [HyperGeometric()].
#' @param n The number of samples to draw. Defaults to `1L`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Unused. Unevaluated arguments will generate a warning to
#' catch mispellings or other possible errors.
#'
#' @family HyperGeometric distribution
#'
#' @return In case of a single distribution object or `n = 1`, either a numeric
#' vector of length `n` (if `drop = TRUE`, default) or a `matrix` with `n` columns
#' (if `drop = FALSE`).
#' @export
#'
random.HyperGeometric <- function(x, n = 1L, drop = TRUE, ...) {
n <- make_positive_integer(n)
if (n == 0L) {
return(numeric(0L))
}
FUN <- function(at, d) rhyper(nn = at, m = d$m, n = d$n, k = d$k)
apply_dpqr(d = x, FUN = FUN, at = n, type = "random", drop = drop)
}
#' Evaluate the probability mass function of a HyperGeometric distribution
#'
#' Please see the documentation of [HyperGeometric()] for some properties
#' of the HyperGeometric distribution, as well as extensive examples
#' showing to how calculate p-values and confidence intervals.
#'
#' @inherit HyperGeometric examples
#'
#' @param d A `HyperGeometric` object created by a call to [HyperGeometric()].
#' @param x A vector of elements whose 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]{dhyper}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family HyperGeometric 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
#'
pdf.HyperGeometric <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) dhyper(x = at, m = d$m, n = d$n, k = d$k, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "density", drop = drop, elementwise = elementwise)
}
#' @rdname pdf.HyperGeometric
#' @export
log_pdf.HyperGeometric <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) dhyper(x = at, m = d$m, n = d$n, k = d$k, log = TRUE)
apply_dpqr(d = d, FUN = FUN, at = x, type = "logLik", drop = drop, elementwise = elementwise)
}
#' Evaluate the cumulative distribution function of a HyperGeometric distribution
#'
#' @inherit HyperGeometric examples
#'
#' @param d A `HyperGeometric` object created by a call to [HyperGeometric()].
#' @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]{phyper}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family HyperGeometric 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.HyperGeometric <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) phyper(q = at, m = d$m, n = d$n, k = d$k, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "probability", drop = drop, elementwise = elementwise)
}
#' Determine quantiles of a HyperGeometric distribution
#'
#' @inherit HyperGeometric examples
#' @inheritParams random.HyperGeometric
#'
#' @param probs A vector of probabilities.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{x} be evaluated
#' at all elements of \code{probs} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{x} and \code{probs} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{qhyper}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(probs)` columns (if `drop = FALSE`). In case of a vectorized
#' distribution object, a matrix with `length(probs)` columns containing all
#' possible combinations.
#' @export
#'
#' @family HyperGeometric distribution
#'
quantile.HyperGeometric <- function(x, probs, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) qhyper(p = at, m = d$m, n = d$n, k = d$k, ...)
apply_dpqr(d = x, FUN = FUN, at = probs, type = "quantile", drop = drop, elementwise = elementwise)
}
#' Return the support of the HyperGeometric distribution
#'
#' @param d An `HyperGeometric` object created by a call to [HyperGeometric()].
#' @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.HyperGeometric <- function(d, drop = TRUE, ...) {
ellipsis::check_dots_used()
min <- apply(cbind(0, d$k - d$n), 1, max)
max <- apply(as.matrix(d)[, c("m", "k"), drop = FALSE], 1, min)
make_support(min, max, d, drop = drop)
}
#' @exportS3Method
is_discrete.HyperGeometric <- function(d, ...) {
ellipsis::check_dots_used()
setNames(rep.int(TRUE, length(d)), names(d))
}
#' @exportS3Method
is_continuous.HyperGeometric <- function(d, ...) {
ellipsis::check_dots_used()
setNames(rep.int(FALSE, length(d)), names(d))
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.