mixnorm {bmixture} | R Documentation |

## Mixture of Normal distribution

### Description

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

### Usage

```
rmixnorm( n = 10, weight = 1, mean = 0, sd = 1 )
dmixnorm( x, weight = 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 ( |

`mean` |
vector of means. |

`sd` |
vector of standard deviations. |

### Details

Sampling from finite mixture of Normal distribution, with density:

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

### 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 )
mean = c( 0 , 10 , 3 )
sd = c( 1 , 1 , 1 )
data = rmixnorm( n = n, weight = weight, mean = mean, sd = sd )
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 )
## End(Not run)
```

*bmixture*version 1.7 Index]