DTIC ADA1024665: Computation of the Integral of pdf

DTIC ADA1024665: Computation of the Integral of

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An efficient automatic procedure is given for evaluating the integral of the bivariate normal density function (IBND) over an arbitrary polygon Pi. The polygon Pi, defined by N points, falls into one or more of the following classes: S, simple polygons; S-bar, limit elements of sequences of uniformly bounded N-sided simple polygons of the same orientation; Pi, arbitrary polygons, including self-intersecting (SI) ones, where S coincides with or belongs to S-bar which coincides with or belongs to Pi. It is not necessary to specify the class beforehand. The method extracts from Pi a set of N exterior angular regions. The IBND is evaluated over each of these, and the results are properly combined to yield IBND for Pi. In case Pi is SI, account must be taken of the number of its ‘primary circuits’ and their orientations. A by-product of the analyses is the evaluation of a function A(Pi).

Another procedure for obtaining the same final results is described for completeness which is not as efficient. It treats an SI polygon by decomposing it into a finite set of S or S-bar type elements. The IBND is evaluated over each of these; the results are properly summed to give the IBND for Pi. In contrast to the first method, the smallest class S, S-bar, Pi to which Pi belongs must be specified for computational efficiency. The Fortran IV programs for both procedures are presently set to yield approximately 3, 6, or 9-decimal-digit accuracy. Fortran IV listings of the programs are given

• Creator/s: Defense Technical Information Center
• Date: 6/1/1980
• Year: 1980
• Book Topics/Themes: DTIC Archive, DiDonato, A R, NAVAL SURFACE WEAPONS CENTER DAHLGREN VA, *INTEGRAL EQUATIONS, *BIVARIATE ANALYSIS, *BIVARIATE DENSITY FUNCTIONS, *NORMAL DISTRIBUTION, COMPUTER PROGRAMS, COMPUTERIZED SIMULATION, MATRICES(MATHEMATICS), SET THEORY, POINTS(MATHEMATICS), POLYGONS, SEQUENCES(MATHEMATICS), DECOMPOSITION, PROBABILITY DENSITY FUNCTIONS, FORTRAN, COVARIANCE

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