rgsm: Simulating realizations from the gamma shape mixture model

In ForestFit: Statistical Modelling for Plant Size Distributions

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,{Θ}) = ∑_{j=1}^{K}ω_j \frac{β^j}{Γ(j)} x^{j-1} \exp\bigl( -β x\bigr),

where Θ=(ω_1,…,ω_K, β)^T is the parameter vector and known constant K is the number of components. The vector of mixing parameters is given by ω=(ω_1,…,ω_K)^T where ω_js sum to one, i.e., ∑_{j=1}^{K}ω_j=1. Here β 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)

ForestFit documentation built on March 7, 2023, 8:27 p.m.