SPA Solution for Order Statistics of Exponential RVs (module_exp_ord.m)
We derive a multidimensional Saddlepoint solution
as an alternative to (7.4).
We consider only the first case (exponential RVs).
This will provide a means of validating the
integral solution of the previous section.
Let
be a PDF defined on the space
.
The saddlepoint approximation is given by [16]

(7.7) 
where
is the joint cumulant
generating function (CGF)
and
is the joint moment function of
,
and
is the Hessian matrix
of
:
and
is the saddle point, the value of
where
Thus, to obtain the SPA, we need the joint CGF
and its first and secondorder partial derivatives.
Subsections
Baggenstoss
20170519