predQuant: Predictive quantile based on the generalized Pareto model

In ExtremeRisks: Extreme Risk Measures

Predictive quantile based on the generalized Pareto model

Description

Bayesian Generalize Pareto-based predictive quantile for continuous and discrete predictive distribution conditioned on intermediate and extreme levels.

Usage

predQuant(
  qlev,
  postsamp,
  threshold,
  lb,
  ub,
  type = c("continuous", "discrete"),
  extrapolation = FALSE,
  p,
  k,
  n
)

Arguments

qlev	double, quantile level
postsamp	a m by 2 matrix with columns containing the posterior samples of scale and shape parameters of the generalized Pareto distribution, respectively
threshold	threshold for the generalized Pareto model, corresponding to the n-kth order statistic of the sample
lb	double, the lower bound of the admissible region for the quantile value
ub	double, the upper bound of the admissible region for the quantile value
type	data type, either "continuous" or "discrete" for count data.
extrapolation	logical; if TRUE, extrapolate using the threshold stability property
p	scalar tail probability for the extrapolation. Must be smaller than k/n (only used if extrapolation=TRUE)
k	integer, number of exceedances for the generalized Pareto (only used if extrapolation=TRUE)
n	integer, number of observations in the full sample. Must be greater than k (only used if extrapolation=TRUE)

Value

a double indicating the value of the quantile

Examples

## Not run: 
# generate data
set.seed(1234)
n <- 500
samp <- evd::rfrechet(n,0,3,4)
# set effective sample size and threshold
k <- 50
threshold <- sort(samp,decreasing = TRUE)[k+1]
# preliminary mle estimates of scale and shape parameters
mlest <- evd::fpot(samp, threshold)
# empirical bayes procedure
proc <- estPOT(
  samp,
  k = k,
  pn = c(0.01, 0.005),
  type = "continuous",
  method = "bayesian",
  prior = "empirical",
  start = as.list(mlest$estimate),
  sig0 = 0.1)
# predictive density estimation
yg <- seq(0, 50, by = 2)
nyg <- length(yg)
predDens_int <- predDens(
  yg,
  proc$post_sample,proc$t,
  "continuous",
  extrapolation=FALSE)
predQuant_int <- predQuant(
  0.5,
  proc$post_sample,
  proc$t,
  proc$t + 0.01,
  50,
  "continuous",
  extrapolation = FALSE)
predDens_ext <- predDens(
  yg,
  proc$post_sample,
  proc$t,
  "continuous",
  extrapolation = TRUE,
  p = 0.001,
  k = k,
  n = n)
predQuant_ext <- predQuant(
  0.5,
  proc$post_sample,
  proc$t,
  proc$t + 0.01,
  100,
  "continuous",
  extrapolation = TRUE,
  p = 0.005,
  k = k,
  n = n)
  
## End(Not run)

ExtremeRisks documentation built on Nov. 5, 2025, 7:05 p.m.