mixgamma {bmixture} R Documentation

## Mixture of Gamma distribution

### Description

Random generation and density function for a finite mixture of Gamma distribution.

### Usage

rmixgamma( n = 10, weight = 1, alpha = 1, beta = 1 )

dmixgamma( x, weight = 1, alpha = 1, beta = 1 )


### Arguments

 n number of observations. x vector of quantiles. weight vector of probability weights, with length equal to number of components (k). This is assumed to sum to 1; if not, it is normalized. alpha vector of non-negative parameters of the Gamma distribution. beta vector of non-negative parameters of the Gamma distribution.

### Details

Sampling from finite mixture of Gamma distribution, with density:

Pr(x|\underline{w}, \underline{\alpha}, \underline{\beta}) = \sum_{i=1}^{k} w_{i} Gamma(x|\alpha_{i}, \beta_{i}),

where

Gamma(x|\alpha_{i}, \beta_{i})=\frac{(\beta_{i})^{\alpha_{i}}}{\Gamma(\alpha_{i})} x^{\alpha_{i}-1} e^{-\beta_{i}x}.

### Value

Generated data as an vector with size n.

### References

Mohammadi, A., Salehi-Rad, M. R., and Wit, E. C. (2013) Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service. Computational Statistics, 28(2):683-700, doi: 10.1007/s00180-012-0323-3

Mohammadi, A., and Salehi-Rad, M. R. (2012) Bayesian inference and prediction in an M/G/1 with optional second service. Communications in Statistics-Simulation and Computation, 41(3):419-435, doi: 10.1080/03610918.2011.588358

rgamma, rmixnorm, rmixt

### Examples

## Not run:
n      = 10000
weight = c( 0.6  , 0.3  , 0.1   )
alpha  = c( 100  , 200  , 300   )
beta   = c( 100/3, 200/4, 300/5 )

data = rmixgamma( n = n, weight = weight, alpha = alpha, beta = beta )

hist( data, prob = TRUE, nclass = 30, col = "gray" )

x            = seq( -20, 20, 0.05 )
densmixgamma = dmixnorm( x, weight, alpha, beta )

lines( x, densmixgamma, lwd = 2 )

## End(Not run)


[Package bmixture version 1.7 Index]