Bayesian Estimation for Finite Mixture of Distributions

Provides statistical tools for Bayesian estimation of mixture distributions, mainly a mixture of Gamma, Normal, and t-distributions. The package is implemented based on the Bayesian literature for the finite mixture of distributions, including Mohammadi and et al. (2013) and Mohammadi and Salehi-Rad (2012) .

bmixture

The R package bmixture provides statistical tools for Bayesian estimation for the mixture of distributions. The package implemented the improvements in the Bayesian literature, including Mohammadi et al. (2013) and Mohammadi and Salehi-Rad (2012). Besides, the package contains several functions for simulation and visualization, as well as a real dataset taken from the literature.

Installation

You can install the latest version from CRAN using:

install.packages( "bmixture" )

require( "bmixture" )

Example 1: Finite mixture of Normal distributions using real world data

Here is a simple example to see the performance of the package for the Finite mixture of Normal distributions for the galaxy dataset:

data( galaxy )

# Runing bdmcmc algorithm for the galaxy dataset      
mcmc_sample = bmixnorm( data = galaxy )

summary( mcmc_sample ) 
plot( mcmc_sample )
print( mcmc_sample )

Example 2: Finite mixture of Normal distributions using simulatoin data

Here is a simple example to see the performance of the package for the Finite mixture of Normal distributions using simulation data. First, we simulate data from the mixture of Normal with 3 components as follow:

n      = 500
mean   = c( 0  , 10 , 3   )
sd     = c( 1  , 1  , 1   )
weight = c( 0.3, 0.5, 0.2 )
    
data = rmixnorm( n = n, weight = weight, mean = mean, sd = sd )
   
# plot for simulation data      
hist( data, prob = TRUE, nclass = 30, col = "gray" )
    
x           = seq( -20, 20, 0.05 )
densmixnorm = dmixnorm( x, weight, mean, sd )
      
lines( x, densmixnorm, lwd = 2 )  

Now, we run the 'bdmcmc' algorithm for the above simulation data set

bmixnorm.obj = bmixnorm( data, k = 3, iter = 1000 )
    
summary( bmixnorm.obj )