tests/testthat/testutils.rmo/R/sample-bivariate.R

In hsloot/rmo: A package for the Marshall-Olkin distribution

# # MIT License
#
# Copyright (c) 2021 Henrik Sloot
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.

## #### Exogenous shock model ####

#' Bivariate implementation
#'
#' @param n Number of samples (> 0)
#' @param d Dimension (== 2)
#' @param intensities Shock intensities (length == 3; all >= 0, any > 0)
#'
#' @examples
#' rmo_esm_bivariate(10, 2, c(0.4, 0.3, 0.2))
#' rmo_esm_bivariate(10, 2, c(1, 1, 0)) ## independence
#' rmo_esm_bivariate(10, 2, c(0, 0, 1)) ## comonotone
#' @include sample-helper.R
#' @export
rmo_esm_bivariate <- function( # nolint
    n, d = 2, intensities = c(1, 1, 0)) {
  stopifnot(
    is.numeric(n) && 1L == length(n) && 0 == n %% 1 && n > 0 &&
      is.numeric(d) && 1L == length(d) && 0 == d %% 1 && d == 2 &&
      is.numeric(intensities) && 3 == length(intensities) &&
      all(intensities >= 0) && any(intensities > 0)
  )

  first_intensity <- intensities[[1]]
  second_intensity <- intensities[[2]]
  combined_intensity <- intensities[[3]]

  out <- matrix(nrow = n, ncol = 2)
  for (i in 1:n) {
    ## individual shock for component 1
    first <- rexp(1, first_intensity)
    ## individual shock for component 2
    second <- rexp(1, second_intensity)
    ## global shock for both components, 1 and 2
    combined <- rexp(1, combined_intensity)

    out[i, ] <- pmin(c(first, second), combined)
  }

  out
}

## #### Exchangeable MO Arnold model ####

#' Bivariate implementation of the exchangeable Arnold model
#'
#' @param n Number of samples (> 0)
#' @param d Dimension (== 2)
#' @param ex_intensities Exchangeable shock intensities
#'   (length == 2; all >= 0, any > 0)
#'
#' @examples
#' rexmo_mdcm_bivariate(10, 2, c(0.4, 0.3))
#' rexmo_mdcm_bivariate(10, 2, c(1, 0)) ## independence
#' rexmo_mdcm_bivariate(10, 2, c(0, 1)) ## comonotone
#' @include sample-helper.R
#' @export
rexmo_mdcm_bivariate <- function( # nolint
    n, d = 2, ex_intensities = c(1, 0)) {
  stopifnot(
    is.numeric(n) && 1L == length(n) && 0 == n %% 1 && n > 0 &&
      is.numeric(d) && 1L == length(d) && 0 == d %% 1 && d == 2 &&
      is.numeric(ex_intensities) && 2 == length(ex_intensities) &&
      all(ex_intensities >= 0) && any(ex_intensities > 0)
  )

  ## convert to unscaled exchangeable intensities
  ex_intensities <- sapply(1:d, function(i) ex_intensities[i] / choose(d, i))

  ## calculate the transition intensities for all states
  first_transition_intensity <- 2 * ex_intensities[[1]] + ex_intensities[[2]]
  second_transition_intensity <- ex_intensities[[1]] + ex_intensities[[2]]
  ## calculate the transition probabilities for all states
  first_transition_prob <- c(2 * ex_intensities[[1]], ex_intensities[[2]]) /
    first_transition_intensity

  out <- matrix(nrow = n, ncol = 2)
  for (k in 1:n) {
    ## sample waiting time and cardinality of next arriving shock
    waiting_time <- rexp(1, rate = first_transition_intensity)
    num_affected <- sample.int(2, 1,
      replace = FALSE,
      prob = first_transition_prob
    )
    out[k, ] <- waiting_time

    if (num_affected < 2) {
      ## if less than two components are affected sample another waiting
      ## time and set the value of the second component accordingly
      waiting_time <- rexp(1, rate = second_transition_intensity)
      out[k, 2] <- out[k, 2] + waiting_time
      ## we do not need it here, but we have to sample another random
      ## integer to keep the random number generators in sync
      num_affected <- sample.int(1, 1, replace = FALSE) ## dummy
    }
    ## use a random permutation to reorder the components
    perm <- sample.int(2, 2, replace = FALSE)
    out[k, ] <- out[k, perm]
  }
  out
}


## #### Armageddon shock model ####

#' Bivariate implementatino of the Armageddon ESM
#'
#' @param n Number of samples (> 0)
#' @param d Dimension (== 2)
#' @param alpha Individual shock rate (>= 0)
#' @param beta Global shock rate (>= 0; alpha + beta > 0)
#'
#' @examples
#' rarmextmo_esm_bivariate(10, 2, 0.5, 0.2)
#' rarmextmo_esm_bivariate(10, 2, 0, 1) ## comonotone
#' rarmextmo_esm_bivariate(10, 2, 1, 0) ## independence
#' @include sample-helper.R
#' @export
rarmextmo_esm_bivariate <- function( # nolint
    n, d = 2, alpha = 1, beta = 0) {
  stopifnot(
    is.numeric(n) && 1L == length(n) && 0 == n %% 1 && n > 0 &&
      is.numeric(d) && 1L == length(d) && 0 == d %% 1 && d == 2 &&
      is.numeric(alpha) && 1L == length(alpha) && alpha >= 0 &&
      is.numeric(beta) && 1L == length(beta) && beta >= 0 &&
      any(c(alpha, beta) > 0)
  )

  out <- matrix(nrow = n, ncol = 2)
  for (k in 1:n) {
    ## sample the global shock
    global_shock <- rexp(1, rate = beta)
    ## sample the individual shocks
    individual_shock_1 <- rexp(1, rate = alpha)
    individual_shock_2 <- rexp(1, rate = alpha)
    out[k, ] <- pmin(
      c(
        individual_shock_1,
        individual_shock_2
      ),
      global_shock
    )
  }

  out
}