Mason, S. J., , J. S. Galpin, , L. Goddard, , N. E. Graham, , and B. Rajartnam, 2007: Conditional exceedance probabilities. Mon. Wea. Rev., 135, 363–372.
A further assumption here is that Γ is sufficient for ξk, that is, ξk are given by Γ and possibly some further randomization independent of Y.