Wishart Distribution

Description

BWishart produces iid draws from the Wishart Density.

Usage

 BWishart(draws,A0,n0)

Arguments

Details

Produces iid draws from the Wishart density. The expected value of the density is given by A0*n0. The expected value for the inverse density is given by $(A0^(-1))/(n0-k-1)$, where k is the dimension of the density.

Value

An array of dimension n*n*draws with iid draws from the Wishart density, where the last dimension is the index for the draws.

Author(s)

Kjell Nygren knygren@us.imshealth.com

Examples

### Wishart Example 

# Set Constants

n0<-20
A<-(0.5+diag(4)+matrix(0.5,4,4))/n0

# Set Number of draws

draws<-1000

# Simulate 10,000 draws 

system.time(out<-BWishart(draws,A,n0))

# Calculate and display means from draws and "known" expectation

outmean<-matrix(0,4,4)

for(i in 1:4){
   for(j in 1:4){
        outmean[i,j]<-mean(out[i,j,1:draws])
                }       
             }

outmean
A*n0

# Calculate Inverse Wishart

outvar<-array(0,c(4,4,draws))

for(k in 1:draws){
        for(i in 1:4){
           for(j in 1:4){
                outvar[1:4,1:4,k]<-solve(out[1:4,1:4,k])
                        }       
                     }
                 }

# Calculate mean, and display simulated and actual mean

outmean2<-matrix(0,4,4)

for(i in 1:4){
   for(j in 1:4){
        outmean2[i,j]<-mean(outvar[i,j,1:draws])
                }       
             }

outmean2

solve(A)/(n0-4-1)