Accession Number : AD0643228

Title :   THE SADDLE POINT METHOD OF APPROXIMATING EXTREME VALUE PROBABILITIES.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS CRUFT LAB

Personal Author(s) : Trafton,Paul

Report Date : OCT 1966

Pagination or Media Count : 68

Abstract : The saddle point method of asymptotic analysis has been used to approximate the probability of extreme values of a random variable assuming that its characteristic function is known. In particular, the author examines the extreme value probabilities of Gaussian and chi square random variables in detail. Also, he applies the saddle point method to determine false alarm probabilities at the output of systems of the form: filter-squarer-filter with a stationary Gaussian input. The results obtained for this problem lead to a better understanding of post-detection filtering. In addition, use is made of a theorem from the theory of Toeplitz forms. This theorem allows us to obtain useful approximations for the characteristic function of square law systems with finite time integrators as the post-nonlinear filter. He inverts these Toeplitz characteristic functions exactly in some cases and in other cases he uses the saddle point method. Graphs of extreme value probabilities obtained both from closed form Toeplitz approximations and by computer evaluation of saddle point approximations are presented. Also, some results obtained by experimental simulation of certain square law systems are presented. Generally speaking, the saddle point method appears to be in error by less than 1 - 2% for probabilities smaller than 10 to the -2. (Author)

Descriptors :   (*INFORMATION THEORY, PROBABILITY), (*STEEPEST DESCENT METHOD, *PROBABILITY), (*COMPLEX VARIABLES, PROBABILITY), STATISTICAL FUNCTIONS, ASYMPTOTIC SERIES

Subject Categories : Statistics and Probability
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE