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#' @name mixgamma
#'
#' @title The Gamma Mixture Distribution
#'
#' @description The gamma mixture density and auxiliary functions.
#'
#' @param ... List of mixture components.
#' @param param Determines how the parameters in the list are
#' interpreted. See details.
#' @param likelihood Defines with what likelihood the Gamma density is used (Poisson or Exp). Defaults to `poisson`.
#' @param m Vector of means of the Gamma mixture components
#' @param s Vector of standard deviations of the gamma mixture components,
#' @param n Vector of sample sizes of the Gamma mixture components.
#' @param drop Delete the dimensions of an array which have only one level.
#' @param object Gamma mixture object.
#' @param probs Quantiles reported by the `summary` function.
#'
#' @details Each entry in the `...` argument list is expected to
#' be a triplet of numbers which defines the weight \eqn{w_k}, first
#' and second parameter of the mixture component \eqn{k}. A triplet
#' can optionally be named which will be used appropriately.
#'
#' The first and second parameter can be given in different
#' parametrizations which is set by the `param` option:
#' \describe{
#' \item{ab}{Natural parametrization of Gamma density (`a`=shape and `b`=rate). Default. }
#' \item{ms}{Mean and standard deviation, \eqn{m=a/b} and \eqn{s=\sqrt{a}/b}.}
#' \item{mn}{Mean and number of observations. Translation to natural
#' parameter depends on the `likelihood` argument. For a Poisson
#' likelihood \eqn{n=b} (and \eqn{a=m \cdot n}{a=m n}), for an Exp
#' likelihood \eqn{n=a} (and \eqn{b=n/m}).}
#' }
#'
#' @family mixdist
#'
#' @return `mixgamma` returns a gamma mixture with the specified mixture components.
#' `ms2gamma` and
#' `mn2gamma` return the equivalent natural `a` and `b` parametrization given
#' parameters `m`, `s`, or `n`.
#'
#' @examples
#' # Gamma mixture with robust and informative component
#' gmix <- mixgamma(rob = c(0.3, 20, 4), inf = c(0.7, 50, 10))
#'
#' # objects can be printed
#' gmix
#' # or explicitly
#' print(gmix)
#'
#' # summaries are defined
#' summary(gmix)
#'
#' # sub-components may be extracted
#' # by component number
#' gmix[[2]]
#' # or component name
#' gmix[["inf"]]
#'
#' # alternative mean and standard deviation parametrization
#' gmsMix <- mixgamma(rob = c(0.5, 8, 0.5), inf = c(0.5, 9, 2), param = "ms")
#'
#' # or mean and number of observations parametrization
#' gmnMix <- mixgamma(rob = c(0.2, 2, 1), inf = c(0.8, 2, 5), param = "mn")
#'
#' # and mixed parametrizations are also possible
#' gfmix <- mixgamma(rob1 = c(0.15, mn2gamma(2, 1)),
#' rob2 = c(0.15, ms2gamma(2, 5)),
#' inf = c(0.7, 50, 10))
NULL
#' @rdname mixgamma
#' @export
mixgamma <- function(
...,
param = c("ab", "ms", "mn"),
likelihood = c("poisson", "exp")
) {
mix <- mixdist3(...)
assert_matrix(mix, nrows = 3, any.missing = FALSE)
param <- match.arg(param)
likelihood <- match.arg(likelihood)
mix[c(2, 3), ] <- switch(
param,
ab = mix[c(2, 3), ],
ms = t(ms2gamma(mix[2, ], mix[3, ], FALSE)),
mn = t(mn2gamma(mix[2, ], mix[3, ], likelihood, FALSE))
)
rownames(mix) <- c("w", "a", "b")
assert_that(all(mix["a", ] > 0))
assert_that(all(mix["b", ] > 0))
class(mix) <- c("gammaMix", "mix")
likelihood(mix) <- likelihood
mix
}
#' @rdname mixgamma
#' @export
ms2gamma <- function(m, s, drop = TRUE) {
b <- m / s^2
ab <- cbind(a = m * b, b = b)
if (drop) ab <- drop(ab)
ab
}
#' @rdname mixgamma
#' @export
mn2gamma <- function(m, n, likelihood = c("poisson", "exp"), drop = TRUE) {
assert_that(all(n >= 0))
likelihood <- match.arg(likelihood)
ab <- switch(
likelihood,
poisson = cbind(a = m * n, b = n),
exp = cbind(a = n, b = n / m)
)
if (drop) ab <- drop(ab)
ab
}
#' @rdname mixgamma
#' @method print gammaMix
#' @param x The mixture to print
#' @export
print.gammaMix <- function(x, ...) {
cat("Univariate Gamma mixture\n")
NextMethod()
}
#' @rdname mixgamma
#' @method print gammaPoissonMix
#' @param x The mixture to print
#' @export
print.gammaPoissonMix <- function(x, ...) {
cat("Univariate Gamma-Poisson mixture\n")
NextMethod()
}
#' @rdname mixgamma
#' @method print gammaExpMix
#' @param x The mixture to print
#' @export
print.gammaExpMix <- function(x, ...) {
cat("Univariate Gamma-Exponential mixture\n")
NextMethod()
}
#' @rdname mixgamma
#' @method summary gammaMix
#' @export
summary.gammaMix <- function(object, probs = c(0.025, 0.5, 0.975), ...) {
p <- object[1, ]
a <- object[2, ]
b <- object[3, ]
m <- a / b
v <- a / b^2
## calculate mean of the second moment
m2 <- v + m^2
## from this we can get the mean and variance of the mixture
mmix <- sum(p * m)
vmix <- sum(p * (m2 - (mmix)^2))
q <- c()
if (length(probs) != 0) {
q <- qmix.gammaMix(object, p = probs)
names(q) <- paste(format(probs * 100, digits = 2), "%", sep = "")
}
c(mean = mmix, sd = sqrt(vmix), q)
}
#' @rdname mixgamma
#' @method summary gammaPoissonMix
#' @export
summary.gammaPoissonMix <- function(object, probs = c(0.025, 0.5, 0.975), ...) {
n <- attr(object, "n")
p <- object[1, ]
a <- object[2, ]
b <- object[3, ] / n
m <- a / b
v <- a * (b + 1) / b^2
## calculate mean of the second moment
m2 <- v + m^2
## from this we can get the mean and variance of the mixture
mmix <- sum(p * m)
vmix <- sum(p * (m2 - (mmix)^2))
q <- qmix.gammaPoissonMix(object, p = probs)
if (length(q) != 0) {
names(q) <- paste(format(probs * 100, digits = 2), "%", sep = "")
}
c(mean = mmix, sd = sqrt(vmix), q)
}
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