pgsm: Computing cumulative distribution function of the gamma shape...

In ForestFit: Statistical Modelling for Plant Size Distributions

Computing cumulative distribution function of the gamma shape mixture model

Description

Computes cumulative distribution function (cdf) of the gamma shape mixture (GSM) model. The general form for the cdf of the GSM model is given by

F(x,{\Theta}) = \sum_{j=1}^{K}\omega_j F(x,j,\beta),

where

F(x,j,\beta) = \int_{0}^{x} \frac{\beta^j}{\Gamma(j)} y^{j-1} \exp\bigl( -\beta y\bigr) dy,

in which \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

pgsm(data, omega, beta, log.p = FALSE, lower.tail = TRUE)

Arguments

data	Vector of observations.
omega	Vector of the mixing parameters.
beta	The rate parameter.
log.p	If TRUE, then log(cdf) is returned.
lower.tail	If FALSE, then 1-cdf is returned.

Value

A vector of the same length as data, giving the cdf of the 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

data<-seq(0,20,0.1)
omega<-c(0.05, 0.1, 0.15, 0.2, 0.25, 0.25)
beta<-2
pgsm(data, omega, beta)

ForestFit documentation built on April 3, 2025, 5:27 p.m.