mixt {bmixture} | R Documentation |

## Mixture of t-distribution

### Description

Random generation and density function for a finite mixture of univariate t-distribution.

### Usage

```
rmixt( n = 10, weight = 1, df = 1, mean = 0, sd = 1 )
dmixt( x, weight = 1, df = 1, mean = 0, sd = 1 )
```

### Arguments

`n` |
number of observations. |

`x` |
vector of quantiles. |

`weight` |
vector of probability weights, with length equal to number of components ( |

`df` |
vector of degrees of freedom (> 0, maybe non-integer). df = Inf is allowed. |

`mean` |
vector of means. |

`sd` |
vector of standard deviations. |

### Details

Sampling from finite mixture of t-distribution, with density:

`Pr(x|\underline{w}, \underline{df}, \underline{\mu}, \underline{\sigma}) = \sum_{i=1}^{k} w_{i} t_{df}(x| \mu_{i}, \sigma_{i}),`

where

` t_{df}(x| \mu, \sigma) = \frac{ \Gamma( \frac{df+1}{2} ) }{ \Gamma( \frac{df}{2} ) \sqrt{\pi df} \sigma } \left( 1 + \frac{1}{df} \left( \frac{x-\mu}{\sigma} \right) ^2 \right) ^{- \frac{df+1}{2} }.`

### 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( 0.3, 0.5, 0.2 )
df = c( 4 , 4 , 4 )
mean = c( 0 , 10 , 3 )
sd = c( 1 , 1 , 1 )
data = rmixt( n = n, weight = weight, df = df, mean = mean, sd = sd )
hist( data, prob = TRUE, nclass = 30, col = "gray" )
x = seq( -20, 20, 0.05 )
densmixt = dmixt( x, weight, df, mean, sd )
lines( x, densmixt, lwd = 2 )
## End(Not run)
```

*bmixture*version 1.7 Index]