ExtremeRisks (version 0.0.5)

extBQuant: Bayesian extreme quantile

Description

Given posterior samples for the parameters of the continuous or discrete generalized Pareto distribution, return the posterior mean and \(1-\alpha\) level credibility intervals of the extreme quantile

Usage

extBQuant(
  threshold,
  postsamp,
  k,
  n,
  retp,
  alpha = 0.05,
  type = c("continuous", "discrete")
)

Value

a list with components

• mQ posterior mean of the extreme quantile

• ciQ vector of dimension 2 returning the \(\alpha/2\) and \(1-\alpha/2\) empirical quantiles of the posterior distribution of the extreme quantile

Arguments

threshold

threshold for the generalized Pareto model, corresponding to the \(n-k\)th order statistic of the sample

postsamp

a m by 2 matrix with columns containing the posterior samples of scale and shape parameters of the generalized Pareto distribution, respectively

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)

retp

double indicating the value of the return period

alpha

level for credibility interval. Default: 0.05 giving 95% credibility intervals

type

string indicating distribution types. Default: c('continuous','discrete')

Examples

if (FALSE) {
# generate data
set.seed(1234)
n <- 500
samp <- evd::rfrechet(500,0,3,4)
# 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$estimate),
  sig0 = 0.1)
# extreme quantile corresponding to a return period of 100
extBQuant(
  proc$t,proc$post_sample,
  k,
  n,
  100,
  0.05,
  type = "continuous")
}