qpRndWishart {qpgraph} | R Documentation

## Random Wishart distribution

### Description

Random generation for the (`n.var * n.var`) Wishart distribution (see Press, 1972) with matrix parameter `A=diag(delta)%*%P%*%diag(delta)` and degrees of freedom `df`.

### Usage

    qpRndWishart(delta=1, P=0, df=NULL, n.var=NULL)

### Arguments

`delta` | a numeric vector of `n.var` positive values. If a scalar is provided then this is extended to form a vector.
`P` | a (`n.var * n.var`) positive definite matrix with unit diagonal. If a scalar is provided then this number is used as constant off-diagonal entry for P.
`df` | degrees of freedom.
`n.var` | dimension of the Wishart matrix. It is required only when both delata and P are scalar.

### Details

The degrees of freedom are `df > n.var-1` and the expected value of the distribution is equal to `df * A`. The random generator is based on the algorithm of Odell and Feiveson (1966).

### Value

A list of two `n.var * n.var` matrices `rW` and `meanW` where `rW` is a random value from the Wishart and `meanW` is the expected value of the distribution.

### Author(s)

A. Roverato

### References

Odell, P.L. and Feiveson, A.G. A numerical procedure to generate a sample covariance matrix. J. Am. Statist. Assoc. 61, 199-203, 1966.

Press, S.J. Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference. New York: Holt, Rinehalt and Winston, 1972.

Tur, I., Roverato, A. and Castelo, R. Mapping eQTL networks with mixed graphical Markov models. Genetics, 198(4):1377-1393, 2014.

### See Also

`qpG2Sigma`

### Examples

    ## Construct an adjacency matrix for a graph on 6 vertices

    nVar <- 6
    A <- matrix(0, nVar, nVar)
    A[1,2] <- A[2,3] <- A[3,4] <- A[3,5] <- A[4,6] <- A[5,6] <- 1
    A=A + t(A)
    A
    set.seed(123)
    M <- qpRndWishart(delta=sqrt(1/nVar), P=0.5, n.var=nVar)
    M
    set.seed(123)
    d=1:6
    M <- qpRndWishart(delta=d, P=0.7, df=20)
    M

[Package qpgraph version 2.20.0 Index]