# pgsm: Computing cumulative distribution function of the gamma shape... In ForestFit: Statistical Modelling for Plant Size Distributions

## 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,{Θ}) = ∑_{j=1}^{K}ω_j F(x,j,β),

where

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

in which 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

 1 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.

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

 1 2 3 4 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 Feb. 6, 2021, 5:05 p.m.