Extended generalized Pareto distribution

Density function, distribution function, quantile function and random number generation for various extended generalized Pareto distributions

Usage

pegp(
  q,
  scale,
  shape,
  kappa,
  model = c("pt-beta", "pt-gamma", "pt-power", "gj-tnorm", "gj-beta", "exptilt",
    "logist"),
  lower.tail = TRUE,
  log.p = FALSE
)

degp(
  x,
  scale,
  shape,
  kappa,
  model = c("pt-beta", "pt-gamma", "pt-power", "gj-tnorm", "gj-beta", "exptilt",
    "logist"),
  log = FALSE
)

qegp(
  p,
  scale,
  shape,
  kappa,
  model = c("pt-beta", "pt-gamma", "pt-power", "gj-tnorm", "gj-beta", "exptilt",
    "logist"),
  lower.tail = TRUE
)

regp(
  n,
  scale,
  shape,
  kappa,
  model = c("pt-beta", "pt-gamma", "pt-power", "gj-tnorm", "gj-beta", "exptilt",
    "logist")
)

Arguments

scale: scale parameter, strictly positive.
shape: shape parameter.
kappa: shape parameter for the tilting distribution.
model: string giving the distribution of the model
lower.tail: logical; if TRUE (default), the lower tail probability \(\Pr(X \leq x)\) is returned.
log.p, log: logical; if FALSE (default), values are returned on the probability scale.
x, q: vector of quantiles
p: vector of probabilities
n: scalar number of observations

References

Papastathopoulos, I. and J. Tawn (2013). Extended generalised Pareto models for tail estimation, Journal of Statistical Planning and Inference 143(3), 131–143, <doi:10.1016/j.jspi.2012.07.001>.

Gamet, P. and Jalbert, J. (2022). A flexible extended generalized Pareto distribution for tail estimation. Environmetrics, 33(6), <doi:10.1002/env.2744>.