hpareto {condmixt} | R Documentation |
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)
y,q |
vector of quantiles |
p |
vector of probabilities |
n |
number of observations |
xi |
tail index parameter, inherited from the GPD |
mu |
location parameter, inherited from the Gaussian |
sigma |
scale parameter, inheristed from the Gaussian |
log |
logical, if TRUE, probabilities |
trunc |
logical, if TRUE (default), the hybrid Pareto density is truncated below zero. |
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.
dhpareto
gives the density, phpareto
gives the
distribution function, qhpareto
gives the quantile function and
rhpareto
generates random deviates.
Julie Carreau
Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Model for Asymmetric Fat-tailed Data: the Univariate Case, 12, Extremes
hpareto.alpha
, hpareto.beta
and
hpareto.gamma