rWishart {bayesSurv} | R Documentation |

## Sample from the Wishart distribution

### Description

Sample from the Wishart distribution

`\mbox{Wishart}(\nu, S),`

where `\nu`

are degrees of freedom of the Wishart distribution
and `S`

is its scale matrix. The same parametrization as in
Gelman (2004) is assumed, that is, if
`W\sim\mbox{Wishart}(\nu,S)`

then

`\mbox{E}(W) = \nu S`

.

In the univariate case, `\mbox{Wishart}(\nu,S)`

is the
same as `\mbox{Gamma}(\nu/2, 1/(2S)).`

Generation of random numbers is performed by the algorithm described in Ripley (1987, pp. 99).

### Usage

```
rWishart(n, df, S)
```

### Arguments

`n` |
number of observations to be sampled. |

`df` |
degrees of freedom of the Wishart distribution. |

`S` |
scale matrix of the Wishart distribution. |

### Value

Matrix with sampled points (lower triangles of `W`

) in rows.

### Author(s)

Arnošt Komárek arnost.komarek@mff.cuni.cz

### References

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004).
*Bayesian Data Analysis, Second edition*.
Boca Raton: Chapman and Hall/CRC.

Ripley, B. D. (1987).
*Stochastic Simulation*.
New York: John Wiley and Sons.

### Examples

```
### The same as rgamma(n, shape=df/2, rate=1/(2*S))
n <- 1000
df <- 1
S <- 3
w <- rWishart(n=n, df=df, S=S)
mean(w) ## should be close to df*S
var(w) ## should be close to 2*df*S^2
### Multivariate Wishart
n <- 1000
df <- 2
S <- matrix(c(1,3,3,13), nrow=2)
w <- rWishart(n=n, df=df, S=S)
apply(w, 2, mean) ## should be close to df*S
df*S
df <- 2.5
S <- matrix(c(1,2,3,2,20,26,3,26,70), nrow=3)
w <- rWishart(n=n, df=df, S=S)
apply(w, 2, mean) ## should be close to df*S
df*S
```

*bayesSurv*version 3.7 Index]