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, Frechet, Gamma, Gompertz, Log-normal, Log-logistic, Lomax, skew-normal, and Weibull.

Usage

rmixture(n, g, K, param)

Value

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

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 $\lambda$.

Author

Mahdi Teimouri

Details

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

Examples

Run this code

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)

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