Added GEV and GPD distributions

DESCRIPTION

@@ -15,6 +15,10 @@ Authors@R:
              family = "Hayes",
              role = c("aut"),
              comment = c(ORCID = "0000-0002-4985-5160")),
+      person(given = "Rob",
+             family = "Hyndman",
+             role = c("aut"),
+             comment = c(ORCID = "0000-0002-2140-5352")),
       person(given = "Earo",
              family = "Wang",
              role = c("ctb"),
@@ -45,6 +49,7 @@ Suggests:
     covr,
     mvtnorm,
     actuar (>= 2.0.0),
+    evd,
     ggdist,
     ggplot2
 RdMacros: 
@@ -54,4 +59,4 @@ BugReports: https://github.com/mitchelloharawild/distributional/issues
 Encoding: UTF-8
 Language: en-GB
 Roxygen: list(markdown = TRUE)
-RoxygenNote: 7.3.1
+RoxygenNote: 7.3.2

NAMESPACE

@@ -138,6 +138,14 @@ S3method(dim,dist_default)
 S3method(dim,dist_multinomial)
 S3method(dim,dist_mvnorm)
 S3method(dimnames,distribution)
+S3method(distributional::cdf,dist_gev)
+S3method(distributional::cdf,dist_gpd)
+S3method(distributional::covariance,dist_gev)
+S3method(distributional::covariance,dist_gpd)
+S3method(distributional::generate,dist_gev)
+S3method(distributional::generate,dist_gpd)
+S3method(distributional::log_density,dist_gev)
+S3method(distributional::log_density,dist_gpd)
 S3method(family,dist_default)
 S3method(family,distribution)
 S3method(format,dist_bernoulli)
@@ -153,6 +161,8 @@ S3method(format,dist_exponential)
 S3method(format,dist_f)
 S3method(format,dist_gamma)
 S3method(format,dist_geometric)
+S3method(format,dist_gev)
+S3method(format,dist_gpd)
 S3method(format,dist_gumbel)
 S3method(format,dist_hypergeometric)
 S3method(format,dist_inflated)
@@ -312,6 +322,8 @@ S3method(mean,dist_exponential)
 S3method(mean,dist_f)
 S3method(mean,dist_gamma)
 S3method(mean,dist_geometric)
+S3method(mean,dist_gev)
+S3method(mean,dist_gpd)
 S3method(mean,dist_gumbel)
 S3method(mean,dist_hypergeometric)
 S3method(mean,dist_inflated)
@@ -408,6 +420,12 @@ S3method(skewness,dist_sample)
 S3method(skewness,dist_uniform)
 S3method(skewness,dist_weibull)
 S3method(skewness,distribution)
+S3method(stats::density,dist_gev)
+S3method(stats::density,dist_gpd)
+S3method(stats::median,dist_gev)
+S3method(stats::median,dist_gpd)
+S3method(stats::quantile,dist_gev)
+S3method(stats::quantile,dist_gpd)
 S3method(sum,distribution)
 S3method(support,dist_categorical)
 S3method(support,dist_default)
@@ -452,6 +470,8 @@ export(dist_exponential)
 export(dist_f)
 export(dist_gamma)
 export(dist_geometric)
+export(dist_gev)
+export(dist_gpd)
 export(dist_gumbel)
 export(dist_hypergeometric)
 export(dist_inflated)

NEWS.md

@@ -13,6 +13,8 @@
 
 * `support()` now shows whether the interval of support is open or 
   closed (@venpopov, #97)
+* Added `dist_gev()` for the Generalised Extreme Value distribution and
+  `dist_gpd()` for the Generalised Pareto distribution (@robjhyndman, #124).
 
 ## Improvements
 

R/dist_gev.R

@@ -0,0 +1,132 @@
+#' The Generalized Extreme Value Distribution
+#'
+#' The GEV distribution function with parameters \eqn{\code{location} = a},
+#' \eqn{\code{scale} = b} and \eqn{\code{shape} = s} is
+#'
+#' \deqn{F(x) = \exp\left[-\{1+s(x-a)/b\}^{-1/s}\right]}
+#'
+#' for \eqn{1+s(x-a)/b > 0}, where \eqn{b > 0}. If \eqn{s = 0} the distribution
+#' is defined by continuity, giving
+#'
+#' \deqn{F(x) = \exp\left[-\exp\left(-\frac{x-a}{b}\right)\right]}
+#'
+#' The support of the distribution is the real line if \eqn{s = 0},
+#' \eqn{x \geq a - b/s} if \eqn{s \neq 0}, and
+#' \eqn{x \leq a - b/s} if \eqn{s < 0}.
+#'
+#' The parametric form of the GEV encompasses that of the Gumbel, Frechet and
+#' reverse Weibull distributions, which are obtained for \eqn{s = 0},
+#' \eqn{s > 0} and \eqn{s < 0} respectively. It was first introduced by
+#' Jenkinson (1955).
+#'
+#' @references Jenkinson, A. F. (1955) The frequency distribution of the annual
+#' maximum (or minimum) of meteorological elements. \emph{Quart. J. R. Met. Soc.},
+#' \bold{81}, 158–171.
+#' @param location the location parameter \eqn{a} of the GEV distribution.
+#' @param scale the scale parameter \eqn{b} of the GEV distribution.
+#' @param shape the shape parameter \eqn{s} of the GEV distribution.
+#' @seealso \code{\link[evd]{gev}}
+#' @examples
+#' dist <- dist_gev(location = 0, scale = 1, shape = 0)
+#' @export
+
+dist_gev <- function(location, scale, shape) {
+  location <- vctrs::vec_cast(unname(location), double())
+  shape <- vctrs::vec_cast(unname(shape), double())
+  scale <- vctrs::vec_cast(unname(scale), double())
+  if (any(scale <= 0)) {
+    stop("The scale parameter of a GEV distribution must be strictly positive")
+  }
+  distributional::new_dist(location = location, scale = scale, shape = shape, class = "dist_gev")
+}
+
+#' @export
+format.dist_gev <- function(x, digits = 2, ...) {
+  sprintf(
+    "GEV(%s, %s, %s)",
+    format(x[["location"]], digits = digits, ...),
+    format(x[["scale"]], digits = digits, ...),
+    format(x[["shape"]], digits = digits, ...)
+  )
+}
+
+#' @exportS3Method distributional::log_density
+log_density.dist_gev <- function(x, at, ...) {
+  z <- (at - x[["location"]]) / x[["scale"]]
+  if (x[["shape"]] == 0) {
+    pdf <- -z - exp(-z)
+  } else {
+    xx <- 1 + x[["shape"]] * z
+    xx[xx <= 0] <- NA_real_
+    pdf <- -xx^(-1 / x[["shape"]]) - (1 / x[["shape"]] + 1) * log(xx)
+    pdf[is.na(pdf)] <- -Inf
+  }
+  pdf - log(x[["scale"]])
+}
+
+#' @exportS3Method stats::density
+density.dist_gev <- function(x, at, ...) {
+  exp(log_density.dist_gev(x, at, ...))
+}
+
+#' @exportS3Method distributional::cdf
+cdf.dist_gev <- function(x, q, ...) {
+  z <- (q - x[["location"]]) / x[["scale"]]
+  if (x[["shape"]] == 0) {
+    exp(-exp(-z))
+  } else {
+    exp(-pmax(1 + x[["shape"]] * z, 0)^(-1 / x[["shape"]]))
+  }
+}
+
+#' @exportS3Method stats::quantile
+quantile.dist_gev <- function(x, p, ...) {
+  if (x[["shape"]] == 0) {
+    x[["location"]] - x[["scale"]] * log(-log(p))
+  } else {
+    x[["location"]] + x[["scale"]] * ((-log(p))^(-x[["shape"]]) - 1) / x[["shape"]]
+  }
+}
+
+#' @exportS3Method distributional::generate
+generate.dist_gev <- function(x, times, ...) {
+  z <- stats::rexp(times)
+  if (x[["shape"]] == 0) {
+    x[["location"]] - x[["scale"]] * log(z)
+  } else {
+    x[["location"]] + x[["scale"]] * (z^(-x[["shape"]]) - 1) / x[["shape"]]
+  }
+}
+
+#' @export
+mean.dist_gev <- function(x, ...) {
+  if (x[["shape"]] == 0) {
+    x[["location"]] + x[["scale"]] * 0.57721566490153286
+  } else if (x[["shape"]] < 1) {
+    x[["location"]] + x[["scale"]] * (gamma(1 - x[["shape"]]) - 1) / x[["shape"]]
+  } else {
+    Inf
+  }
+}
+
+#' @exportS3Method stats::median
+median.dist_gev <- function(x, ...) {
+  if (x[["shape"]] == 0) {
+    x[["location"]] - x[["scale"]] * log(log(2))
+  } else {
+    x[["location"]] + x[["scale"]] * (log(2)^(-x[["shape"]]) - 1) / x[["shape"]]
+  }
+}
+
+#' @exportS3Method distributional::covariance
+covariance.dist_gev <- function(x, ...) {
+  if (x[["shape"]] == 0) {
+    x[["scale"]]^2 * pi^2 / 6
+  } else if (x[["shape"]] < 0.5) {
+    g2 <- gamma(1 - 2 * x[["shape"]])
+    g1 <- gamma(1 - x[["shape"]])
+    x[["scale"]]^2 * (g2 - g1^2) / x[["shape"]]^2
+  } else {
+    Inf
+  }
+}

R/dist_gpd.R

@@ -0,0 +1,124 @@
+#' The Generalized Pareto Distribution
+#'
+#' The GPD distribution function with parameters \eqn{\code{location} = a},
+#' \eqn{\code{scale} = b} and \eqn{\code{shape} = s} is
+#'
+#' \deqn{F(x) = 1 - \left(1+s(x-a)/b\right)^{-1/s}}
+#'
+#' for \eqn{1+s(x-a)/b > 0}, where \eqn{b > 0}. If \eqn{s = 0} the distribution
+#' is defined by continuity, giving
+#'
+#' \deqn{F(x) = 1 - \exp\left(-\frac{x-a}{b}\right)}
+#'
+#' The support of the distribution is \eqn{x \geq a} if \eqn{s \geq 0}, and
+#' \eqn{a \leq x \leq a -b/s} if \eqn{s < 0}.
+#'
+#' The Pickands–Balkema–De Haan theorem states that for a large class of
+#' distributions, the tail (above some threshold) can be approximated by a GPD.
+#'
+#' @param location the location parameter \eqn{a} of the GPD distribution.
+#' @param scale the scale parameter \eqn{b} of the GPD distribution.
+#' @param shape the shape parameter \eqn{s} of the GPD distribution.
+#' @seealso \code{\link[evd]{gpd}}
+#' @examples
+#' dist <- dist_gpd(location = 0, scale = 1, shape = 0)
+#' @export
+
+dist_gpd <- function(location, scale, shape) {
+  location <- vctrs::vec_cast(unname(location), double())
+  shape <- vctrs::vec_cast(unname(shape), double())
+  scale <- vctrs::vec_cast(unname(scale), double())
+  if (any(scale <= 0)) {
+    stop("The scale parameter of a GPD distribution must be strictly positive")
+  }
+  distributional::new_dist(location = location, scale = scale, shape = shape, class = "dist_gpd")
+}
+
+#' @export
+format.dist_gpd <- function(x, digits = 2, ...) {
+  sprintf(
+    "GPD(%s, %s, %s)",
+    format(x[["location"]], digits = digits, ...),
+    format(x[["scale"]], digits = digits, ...),
+    format(x[["shape"]], digits = digits, ...)
+  )
+}
+
+#' @exportS3Method distributional::log_density
+log_density.dist_gpd <- function(x, at, ...) {
+  z <- (at - x[["location"]]) / x[["scale"]]
+  if (x[["shape"]] == 0) {
+    pdf <- -z
+  } else {
+    xx <- 1 + x[["shape"]] * z
+    xx[xx <= 0] <- NA_real_
+    pdf <- -(1 / x[["shape"]] + 1) * log(xx)
+    pdf[is.na(pdf)] <- -Inf
+  }
+  if (x[["shape"]] >= 0) {
+    pdf[z < 0] <- -Inf
+  } else {
+    pdf[z < 0 | z > -1 / x[["shape"]]] <- -Inf
+  }
+  pdf - log(x[["scale"]])
+}
+
+#' @exportS3Method stats::density
+density.dist_gpd <- function(x, at, ...) {
+  exp(log_density.dist_gpd(x, at, ...))
+}
+
+#' @exportS3Method distributional::cdf
+cdf.dist_gpd <- function(x, q, ...) {
+  z <- pmax(q - x[["location"]], 0) / x[["scale"]]
+  if (x[["shape"]] == 0) {
+    1 - exp(-z)
+  } else {
+    1 - pmax(1 + x[["shape"]] * z, 0)^(-1 / x[["shape"]])
+  }
+}
+
+#' @exportS3Method stats::quantile
+quantile.dist_gpd <- function(x, p, ...) {
+  if (x[["shape"]] == 0) {
+    x[["location"]] - x[["scale"]] * log(1 - p)
+  } else {
+    x[["location"]] + x[["scale"]] * ((1 - p)^(-x[["shape"]]) - 1) / x[["shape"]]
+  }
+}
+
+#' @exportS3Method distributional::generate
+generate.dist_gpd <- function(x, times, ...) {
+  if (x[["shape"]] == 0) {
+    x[["location"]] + x[["scale"]] * stats::rexp(times)
+  } else {
+    quantile(x, stats::runif(times))
+  }
+}
+
+#' @export
+mean.dist_gpd <- function(x, ...) {
+  if (x[["shape"]] < 1) {
+    x[["location"]] + x[["scale"]] / (1 - x[["shape"]])
+  } else {
+    Inf
+  }
+}
+
+#' @exportS3Method stats::median
+median.dist_gpd <- function(x, ...) {
+  if (x[["shape"]] == 0) {
+    x[["location"]] - x[["scale"]] * log(0.5)
+  } else {
+    x[["location"]] + x[["scale"]] * (2^x[["shape"]] - 1) / x[["shape"]]
+  }
+}
+
+#' @exportS3Method distributional::covariance
+covariance.dist_gpd <- function(x, ...) {
+  if (x[["shape"]] < 0.5) {
+    x[["scale"]]^2 / (1 - x[["shape"]])^2 / (1 - 2 * x[["shape"]])
+  } else {
+    Inf
+  }
+}