condmixt (version 1.1)

hpareto.alpha: Auxillary Parameters of the Hybrid Pareto Distribution

Description

Computes the junction point alpha, the GPD scale parameter beta and the normalization factor gamma of the hybrid Pareto distributions.

Usage

hpareto.alpha(xi, mu = 0, sigma = 1)
hpareto.beta(xi, sigma = 1)
hpareto.gamma(xi, mu = 0, sigma = 1, trunc = T)

Arguments

xi

Tail index parameter of the hybrid Pareto distribution.

mu

Location parameter of the hybrid Pareto distribution.

sigma

Scale parameter of the hybrid Pareto distribution.

trunc

Binary variable : if TRUE, the density of the hybrid Pareto is truncated below zero

Value

Computation of the auxillary parameters alpha, beta and gamma.

Details

Let z = (1+xi)^2/(2 pi) and W be the Lambert W function implemented in lambertw. Then : alpha = mu + sigma * sqrt(W(z)), beta = sigma * |1 + xi| / sqrt(W(z)) and gamma is the integral from 0 (is trunc is true, -infinity otherwise) to alpha.

References

Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Model for Asymmetric Fat-tailed Data: the Univariate Case, 12, Extremes

See Also

dhpareto,phpareto and rhpareto

Examples

# NOT RUN {
hpareto.alpha(0.1,0,1)
hpareto.beta(0.1,1)
hpareto.gamma(0.1,0,1)
# }