bvhar (version 2.2.2)

sim_iw: Generate Inverse-Wishart Random Matrix

Description

This function samples one matrix IW matrix.

Usage

sim_iw(mat_scale, shape)

Value

One k x k matrix following IW distribution

Arguments

mat_scale

Scale matrix

shape

Shape

Details

Consider $\mathrm{\Sigma }\sim IW(\mathrm{\Psi },\nu )$.

1. Upper triangular Bartlett decomposition: k x k matrix $Q=[q_{ij}]$ upper triangular with

   1. $q_{ii}^2{\chi }_{\nu -i+1}^2$

   2. $q_{ij}\sim N(0,1)$ with i < j (upper triangular)

2. Lower triangular Cholesky decomposition: $\mathrm{\Psi }=L{L}^T$

3. $A=L(Q^{-1}{)}^T$

4. $\mathrm{\Sigma }=A{A}^T\sim IW(\mathrm{\Psi },\nu )$