For modules using a fixed reference hypothesis,
care must be taken in calculation of the
J-function because the data is more often than not
in the tails of the PDF. For fixed reference hypotheses
the J function is
Fixed reference hypothesis
The numerator density is usually of a simple form
so it is known exactly.
The denominator density
must be known exactly
or approximated carefully so that it is accurate even in the far tails
of the PDF. The SPA (Section 2.3.2),
provides a solution for cases when the
exact PDF cannot be derived, but the exact
moment-generating function (MGF) is known.
The SPA is known to be accurate
in the far tails of the PDF .