The saddlepoint vector is the solution to the equation

where is the diagonal matrix with diagonal element equal to , written compactly (borrowing efficient MATLAB notation) as

where are the elements of vector defined by

where is a vector of 1's.

The saddlepoint approximation for is given by

where operates separately on each element and

where

where borrows the efficient MATLAB notation for element-wise exponentiation by .

To find the saddlepoint, we initialize to zeros, then implement the iterative Newton-Raphson search for the saddlepoint as described in [16]. For convenience, a MATLAB implementation is provided below in section 16.6.3.

Baggenstoss 2017-05-19