6.3.9.6.5.1.2. statsmodels.sandbox.distributions.mv_normal.MVT.affine_transformed¶

MVT.affine_transformed(shift, scale_matrix)[source]¶

return distribution of a full rank affine transform

for full rank scale_matrix only

Parameters:

shift : array_like

shift of mean

scale_matrix : array_like

linear transformation matrix

Returns:

mvt : instance of MVT

instance of multivariate t distribution given by affine transformation

Notes

This checks for eigvals<=0, so there are possible problems for cases with positive eigenvalues close to zero.

I’m not sure about general case, non-full rank transformation are not multivariate t distributed.

y = a + B x

where a is shift, B is full rank scale matrix with same dimension as sigma