hpareto {condmixt} R Documentation

## The Hybrid Pareto Distribution

### Description

Density, distribution function, quantile function and random generation for the hybrid Pareto distribution with parameters xi, mu and sigma.

### Usage

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)


### Arguments

 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 p are given as log(p). trunc logical, if TRUE (default), the hybrid Pareto density is truncated below zero.

### Details

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.

### Value

dhpareto gives the density, phpareto gives the distribution function, qhpareto gives the quantile function and rhpareto generates random deviates.

Julie Carreau

### References

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