Density, distribution function, quantile function and random generation for the hybrid Pareto distribution with parameters xi, mu and sigma.
dhpareto(y, xi, mu = 0, sigma = 1, log = FALSE, trunc = TRUE)
phpareto(q, xi, mu = 0, sigma = 1, trunc = TRUE)
qhpareto(p, xi, mu = 0, sigma = 1, trunc = TRUE)
rhpareto(n, xi, mu = 0, sigma = 1, trunc = TRUE)
vector of quantiles
vector of probabilities
number of observations
tail index parameter, inherited from the GPD
location parameter, inherited from the Gaussian
scale parameter, inheristed from the Gaussian
logical, if TRUE, probabilities p
are
given as log(p
).
logical, if TRUE (default), the hybrid Pareto density is truncated below zero.
dhpareto
gives the density, phpareto
gives the
distribution function, qhpareto
gives the quantile function and
rhpareto
generates random deviates.
The hybrid Pareto density is given by a Gaussian with parameters
mu
and sigma
below the threshold
alpha (see the function hpareto.alpha
) and by the GPD with
parameters xi
and beta.(see the function
hpareto.beta
) To
ensure continuity of the density and of its derivative at the threshold,
alpha and beta are appropriate functions of xi
, mu
and
sigma
. Appropriate reweighting factor gamma ensures that the
density integrate to one.
Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Model for Asymmetric Fat-tailed Data: the Univariate Case, 12, Extremes