Computation of the Integral of the Bivariate Normal Distribution Over Convex Polygons

Abstract

Next article Computation of the Integral of the Bivariate Normal Distribution Over Convex PolygonsA. R. Didonato, M. P. Jarnagin, Jr., and R. K. HagemanA. R. Didonato, M. P. Jarnagin, Jr., and R. K. Hagemanhttps://doi.org/10.1137/0901010PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA method for computing the integral of the bivariate normal density function over a convex polygon is given. A comparison with two recently published methods is made.[1] D. E. Amos, On computation of the bivariate normal distribution, Math. Comp., 23 (1969), 655–659 40:996 0293.65006 CrossrefISIGoogle Scholar[2] H. L. Crutcher, Bivariate Normal Offset Circle Probability Tables, Vol. III, Applications to Geophysical Data (National Weather Records Center, U.S. Dept. of Commerce. CAL No. XM-2464-G-1), Cornell Aeronautical Laboratory, Inc., Buffalo, NY, 1967 Google Scholar[3] D. J. Daley, Computation of bi-and tri-variate normal integrals, Appl. Statist., 23 (1974), 435–438 CrossrefISIGoogle Scholar[4] A. R. DiDonato, , M. P. Jarnagin, Jr. and , R. K. Hageman, Computation of the Bivariate Normal Distribution over Convex Polygons, Technical Report, NSWC/DL TR-3886, Naval Surface Weapons Center, Dahlgren, VA 22448, 1978, September Google Scholar[5] Z. Drezner, Computation of the bivariate normal integral, Math. Comp., 32 (1978), 277–279 57:1833 0378.33002 CrossrefISIGoogle Scholar[6] R. A. Gideon and , J. Gurland, A Method of Obtaining the Bivariate Normal Probability Over an Arbitrary Polygon, Tech. Rept., 304, Dept. of Statistics, University of Wisconsin, Madison, WI, 1972, May Google Scholar[7] Rudy A. Gideon and , John Gurland, A polynomial type approximation for bivariate normal variates, SIAM J. Appl. Math., 34 (1978), 681–684 10.1137/0134055 57:10917 0387.62045 LinkISIGoogle Scholar[8] R. R. Sowden and , D. Secrest, Computation of the bi-variate normal integral, J. Roy. Statist. Soc. Ser. C Appl. Statist., 18 (1969), 169–180 40:953 CrossrefISIGoogle Scholar[9] N. M. Steen, , G. O. Byrne and , E. M. Gelbard, Gaussian quadratures formulas, Math. Comp., 23 (1969), 661–671 0187.12902 ISIGoogle Scholar[10] Google ScholarKeywordsProbability: special processesgeometric probability applications; statistics multivariate analysis Next article FiguresRelatedReferencesCited byDetails Short-Term Collision Probability Algorithm for Parallelepiped-Shaped SatellitesJournal of Guidance, Control, and Dynamics, Vol. 45, No. 6 Cross Ref Trajectory Risk Modelling and Planning for Unmanned Cargo Aircraft3 November 2021 Cross Ref Uncertainty in Continuous Scatterplots, Continuous Parallel Coordinates, and FibersIEEE Transactions on Visualization and Computer Graphics, Vol. 27, No. 2 Cross Ref Probabilities in a Gaussian Cocked Hat27 March 2019 | Journal of Navigation, Vol. 72, No. 06 Cross Ref Variable Resolution Occupancy Mapping Using Gaussian Mixture ModelsIEEE Robotics and Automation Letters, Vol. 4, No. 2 Cross Ref References6 November 2017 Cross Ref Computing Gaussian & exponential measures of semi-algebraic setsAdvances in Applied Mathematics, Vol. 91 Cross Ref Performance of Some Resistant Rules for Outlier LabelingJournal of the American Statistical Association, Vol. 81, No. 396 Cross Ref Improved approximation for multinormal integralStructural Safety, Vol. 4, No. 2 Cross Ref A Method for Computing the Integral of the Bivariate Normal Distribution Over an Arbitrary PolygonA. R. DiDonato and R. K. Hageman16 May 2012 | SIAM Journal on Scientific and Statistical Computing, Vol. 3, No. 4AbstractPDF (1236 KB) Volume 1, Issue 2| 1980SIAM Journal on Scientific and Statistical Computing History Submitted:25 May 1979Published online:14 July 2006 InformationCopyright © 1980 Society for Industrial and Applied MathematicsKeywordsProbability: special processesgeometric probability applications; statistics multivariate analysisPDF Download Article & Publication DataArticle DOI:10.1137/0901010Article page range:pp. 179-186ISSN (print):0196-5204ISSN (online):2168-3417Publisher:Society for Industrial and Applied Mathematics