Time delay statistics for finite number of channels in all symmetry classes

Within a random matrix theory approach, we obtain spectral statistics of the Wigner time delay $Q$, for arbitrary channels number $M$ and all symmetry classes, in fact general Dyson parameter $\beta$. We also put forth two conjectures: one is related to large-$M$ expansion joint cumulants traces powers which generalizes implies previous conjecture Cunden, Mezzadri, Vivo Simm; other concerns tail distribution $Q$.