ForestFit (version 0.4)

rmixture: Generating random realizations from the well-known mixture models

Description

Generates iid realizations from the mixture model with pdf given by $$f(x,{\Theta}) = \sum_{j=1}^{K}\omega_j f(x,\theta_j),$$ where \(K\) is the number of components, \(\theta_j\), for \(j=1,\dots,K\) is parameter space of the \(j\)-th component, i.e. \(\theta_j=(\alpha_j,\beta_j)^{T}\), and \(\Theta\) is the whole parameter vector \(\Theta=(\theta_1,\dots,\theta_K)^{T}\). Parameters \(\alpha\) and \(\beta\) are the shape and scale parameters or both are the shape parameters. In the latter case, parameters \(\alpha\) and \(\beta\) are called the first and second shape parameters, respectively. We note that the constants \(\omega_j\)s sum to one, i.e., \(\sum_{j=1}^{K}\omega_j=1\). The families considered for the cdf \(f\) include Birnbaum-Saunders, Burr type XII, Chen, F, Fr\'echet, Gamma, Gompertz, Log-normal, Log-logistic, Lomax, skew-normal, and Weibull.

Usage

rmixture(n, g, K, param)

Arguments

n

Number of requested random realizations.

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 \(\lambda\).

Value

A vector of length \(n\), giving a sequence of random realizations from given mixture model.

Details

For the skew-normal case, \(\alpha\), \(\beta\), and \(\lambda\) are the location, scale, and skewness parameters, respectively.

Examples

# NOT RUN {
n<-50
K<-2
weight<-c(0.3,0.7)
alpha<-c(1,2)
beta<-c(2,1)
param<-c(weight,alpha,beta)
rmixture(n, "weibull", K, param)
# }