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 ( |

`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`

.

### Author(s)

Reza Mohammadi a.mohammadi@uva.nl

### 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

### See Also

### 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)
```

*bmixture*version 1.7 Index]