pmixture: Computing cumulative distribution function of the well-known...

In ForestFit: Statistical Modelling for Plant Size Distributions

Computing cumulative distribution function of the well-known mixture models

Description

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

F(x,{Θ}) = ∑_{j=1}^{K}ω_j F(x,θ_j),

where Θ=(θ_1,…,θ_K)^T, is the whole parameter vector, θ_j for j=1,…,K is the parameter space of the j-th component, i.e. θ_j=(α_j,β_j)^{T}, F_j(.,θ_j) is the cdf of the j-th component, 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. Parameters α and β are the shape and scale parameters or both are the shape parameters. In the latter case, the parameters α and β are called the first and second shape parameters, respectively. The families considered for each component include Birnbaum-Saunders, Burr type XII, Chen, F, Frechet, Gamma, Gompertz, Log-normal, Log-logistic, Lomax, skew-normal, and Weibull.

Usage

pmixture(data, g, K, param)

Arguments

data	Vector of observations.
g	Name of the family including: "birnbaum-saunders", "burrxii", "chen", "f", "frechet", "gamma", "gompetrz", "log-normal", "log-logistic", "lomax", "skew-normal", and "weibull".
K	Number of components.
param	Vector of the ω, α, β, and λ.

Details

For the skew-normal case, α, β, and λ are the location, scale, and skewness parameters, respectively.

Value

A vector of the same length as data, giving the cdf of the mixture model computed at data.

Author(s)

Mahdi Teimouri

Examples

data<-seq(0,20,0.1)
K<-2
weight<-c(0.6,0.4)
alpha<-c(1,2)
beta<-c(2,1)
param<-c(weight,alpha,beta)
pmixture(data, "weibull", K, param)

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