Description Usage Arguments Details Value Author(s) References Examples
Density function, distribution function, quantile function, random generation.
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x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
eta |
first shape parameter. |
delta |
nuisance parameter. |
rho, tau |
second shape parameter. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
control |
A list of control paremeters. See section Details. |
The extended Pareto distribution is defined by the following density
f(x) = 1/η x^{-1/η-1}[1+δ(1-x^{-τ})]^{-1/η-1}[1+δ(1-(1-τ)x^{-τ})]
for all x>1 when parametrized by τ. However, a typical parametrization is obtained by setting τ=-ρ/η, i.e.
f(x) = 1/η x^{-1/η-1}[1+δ(1-x^{ρ/η})]^{-1/η-1}[1+δ(1-(1+ρ/η)x^{ρ/η})]
for all x>1 when parametrized by ρ.
The control
argument is a list that can supply any of the
following components:
upperbound
The upperbound used in the optimize
function
when computing numerical quantiles, default to 1e6
.
tol
the desired accuracy used in the optimize
function
when computing numerical quantiles, default to 1e-9
.
dEPD
gives the density,
pEPD
gives the distribution function,
qEPD
gives the quantile function, and
rEPD
generates random deviates.
The length of the result is determined by n
for
rEPD
, and is the maximum of the lengths of the
numerical parameters for the other functions.
The numerical parameters other than n
are recycled to the
length of the result. Only the first elements of the logical
parameters are used.
Christophe Dutang
J. Beirlant, E. Joossens, J. Segers (2009), Second-order refined peaks-over-threshold modelling for heavy-tailed distributions, Journal of Statistical Planning and Inference, Volume 139, Issue 8, Pages 2800-2815.
C. Dutang, Y. Goegebeur, A. Guillou (2014), Robust and bias-corrected estimation of the coefficient of tail dependence, Insurance: Mathematics and Economics
This work was supported by a research grant (VKR023480) from VILLUM FONDEN and an international project for scientific cooperation (PICS-6416).
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