# mixnorm: Mixture of Normal distribution In bmixture: Bayesian Estimation for Finite Mixture of Distributions

## Description

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

## Usage

 ```1 2 3 4``` ``` 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 (k). This is assumed to sum to 1; if not, it is normalized. `mean ` vector of means. `sd ` vector of standard deviations.

## Details

Sampling from finite mixture of Normal distribution, with density:

Pr(x|\underline{w}, \underline{μ}, \underline{σ}) = ∑_{i=1}^{k} w_{i} N(x|μ_{i}, σ_{i}).

## 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

`rnorm`, `rmixt`, `rmixgamma`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## 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) ```