Generating realization from finite mixture models.
Description
The density function of a restricted G-component finite mixture model can be represented as
M(y∣Ψ)=∑g=1GωgfY(y,Θg),
where positive constants ω1,ω2,⋯,ωG are called weight (or mixing proportions) parameters with this properties that ∑g=1Gωg=1 and Ψ=(Θ1,⋯,ΘG)⊤ with Θg=(ωg,μg,Σg,λg)⊤. Herein, fY(y,Θg) accounts for the density function of random vector Y within g-th component that admits the representation given by
Y=dμg+Wλg∣Z0∣+WΣg21Z1,
where μg∈Rd is location vector, λg∈Rd is skewness vector, and Σg is a positive definite symmetric dispersion matrix for g=1,⋯,G. Further, W is a positive random variable with mixing density function fW(w∣θg), Z0∼N(0,1), and Z1∼Nd(0,Σg). We note that W, Z0, and Z1 are mutually independent.
Usage
rmix(n, G, weight, model = "restricted", mu, sigma, lambda, family = "constant",
theta = NULL)
Arguments
n
number of realizations.
G
number of components.
weight
a vector of weight parameters (or mixing proportions).
model
It must be "canonical", "restricted", or "unrestricted". By default model="restricted".
mu
a list of location vectors of G components.
sigma
a list of dispersion matrices of G components.
lambda
a list of skewness vectors of G components. If mixture model is symmetric, then a vector of zeros of appropriate size should be considered for the skewness vector of the corresponding component.
family
name of mixing distribution. By default family = "constant" that corresponds to the finite mixture of multivariate normal (or skew normal) distribution. Other candidates for family name are: "bs" (for Birnbaum-Saunders), "burriii" (for Burr type iii), "chisq" (for chi-square), "exp" (for exponential), "f" (for Fisher), "gamma" (for gamma), "gigaussian" (for generalized inverse-Gaussian), "igamma" (for inverse-gamma), "igaussian" (for inverse-Gaussian), "lindley" (for Lindley), "loglog" (for log-logistic), "lognorm" (for log-normal), "lomax" (for Lomax), "pstable" (for positive α-stable), "ptstable" (for polynomially tilted α-stable), "rayleigh" (for Rayleigh), and "weibull" (for Weibull).
theta
a list of maximum likelihood estimator(s) for θ (parameter vector of mixing distribution) across G components. By default it is NULL.
Value
a matrix with n rows and d+1 columns. The first d columns constitute n realizations from random vector Y=(Y1,⋯,Yd)⊤ and the last column is the label of realization Yi ( for i=1,⋯n ) indicating the component that Yi is coming from.