pmixture {ForestFit}

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

where \Theta=(\theta_1,\dots,\theta_K)^T, is the whole parameter vector, \theta_j for j=1,\dots,K is the parameter space of the j-th component, i.e. \theta_j=(\alpha_j,\beta_j)^{T}, F_j(.,\theta_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 \omega=(\omega_1,\dots,\omega_K)^T where \omega_js sum to one, i.e., \sum_{j=1}^{K}\omega_j=1. Parameters \alpha and \beta are the shape and scale parameters or both are the shape parameters. In the latter case, the parameters \alpha and \beta 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 \omega, \alpha, \beta, and \lambda.

Details

For the skew-normal case, \alpha, \beta, and \lambda 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)