sim_iw {bvhar}R Documentation

Generate Inverse-Wishart Random Matrix

Description

This function samples one matrix IW matrix.

Usage

sim_iw(mat_scale, shape)

Arguments

mat_scale

Scale matrix

shape

Shape

Details

Consider ΣIW(Ψ,ν)\Sigma \sim IW(\Psi, \nu).

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

    1. qii2χνi+12q_{ii}^2 \chi_{\nu - i + 1}^2

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

  2. Lower triangular Cholesky decomposition: Ψ=LLT\Psi = L L^T

  3. A=L(Q1)TA = L (Q^{-1})^T

  4. Σ=AATIW(Ψ,ν)\Sigma = A A^T \sim IW(\Psi, \nu)

Value

One k x k matrix following IW distribution


[Package bvhar version 2.0.1 Index]