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.
SPA Solution for Order Statistics of Exponential RVs (module_exp_ord.m)
be a PDF defined on the space
The saddlepoint approximation is given by 
is the joint cumulant
generating function (CGF)
is the joint moment function of
is the Hessian matrix
is the saddle point, the value of
Thus, to obtain the SPA, we need the joint CGF
and its first and second-order partial derivatives.