GSM (version 1.3.2)

GSMDist: Utility Function

Description

Function evaluations for a Gamma Shape Mixture Model.

Usage

dgsm(x, weight, rateparam) pgsm(q, weight, rateparam, lower.t = TRUE) rgsm(n, weight, rateparam) qgsm(p, x = NULL, weight, rateparam, alpha = .05, br = c(0, 1000), lower.t = TRUE)

Arguments

x, q

vector of quantiles.

n

number of observations.

p

vector of probabilities.

weight

vector of mixture weights.

rateparam

reciprocal of the shape parameter, as in GammaDist.

alpha

outside the interval (alpha, 1 - alpha) the quantiles are found by searching for the root of F(x) - p = 0.

br

a vector containing the end-points of the interval to be searched for the root.

lower.t

logical; if TRUE (default), probabilities are P[X <= x]<="" em=""> otherwise, P[X > x].

Value

dgsm gives the density, pgsm gives the distribution function, qgsm gives the quantile function, and rgsm generates random deviates.

Details

The parametrisation implemented in this function is described in Venturini et al. (2008).

References

Venturini, S., Dominici, F. and Parmigiani, G. (2008), "Gamma shape mixtures for heavy-tailed distributions". Annals of Applied Statistics, Volume 2, Number 2, 756--776. http://projecteuclid.org/euclid.aoas/1215118537

See Also

dgamma, pgamma, rgamma, uniroot.