rgsm {ForestFit}

Simulating realizations from the gamma shape mixture model

Description

Simulates realizations from a gamma shape mixture (GSM) model with probability density function given by

f(x,{\Theta}) = \sum_{j=1}^{K}\omega_j \frac{\beta^j}{\Gamma(j)} x^{j-1} \exp\bigl( -\beta x\bigr),

where \Theta=(\omega_1,\dots,\omega_K, \beta)^T is the parameter vector and known constant K is the number of components. The vector of mixing parameters is given by \omega=(\omega_1,\dots,\omega_K)^T where \omega_js sum to one, i.e., \sum_{j=1}^{K}\omega_j=1. Here \beta is the rate parameter that is equal for all components.

Usage

rgsm(n, omega, beta)

Arguments

n

Number of requested random realizations.

omega

Vector of the mixing parameters.

beta

The rate parameter.

Value

A vector of length n, giving random generated values from GSM model.

Author(s)

Mahdi Teimouri

References

S. Venturini, F. Dominici, and G. Parmigiani, 2008. Gamma shape mixtures for heavy-tailed distributions, The Annals of Applied Statistics, 2(2), 756–776.

Examples

n<-100
omega<-c(0.05, 0.1, 0.15, 0.2, 0.25, 0.25)
beta<-2
rgsm(n, omega, beta)