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For a non-integer number of degrees of freedom $\nu > p-1$, one can simulate the central Wishart distribution $W_p(\nu, \Sigma)$ with the help of the Bartlett decomposition.

How to simulate the noncentral Wishart distribution $W_p(\nu, \Sigma, \Theta)$ for such a $\nu$?

For $\nu>2p-1$ it suffices to apply the equality $W_p(\nu, \Sigma, \Theta) = W_{p}(\nu-p, \Sigma) \ast W_{p}(p, \Sigma, \Theta)$. How to do in the case when $p-1 < \nu \leq 2p-1$?

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