mixgamma function

Mixture of Gamma distribution

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

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:

where

Returns

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, tools:::Rd_expr_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, tools:::Rd_expr_doi("10.1080/03610918.2011.588358")

Author(s)

Reza Mohammadi a.mohammadi@uva.nl

See Also

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)