Recursive Calculation Model for a Special Multivariate Normal Probability of First-Order Stationary Sequence

Published Online:https://doi.org/10.1287/ijoc.2018.0852

References

  • Ambartzumian R, Der Kiureghian A, Ohaniana V, Sukiasiana H (1998) Multinormal probability by sequential conditioned importance sampling: Theory and application. Probab. Engrg. Mech. 13(4):299–308.CrossrefGoogle Scholar
  • Caflisch RE (1998) Monte Carlo and quasi-Monte Carlo methods. Acta Numerica 7:1–49.CrossrefGoogle Scholar
  • Craig P (2008) A new reconstruction of multivariate normal orthant probabilities. J. Royal Statist. Soc. Ser. B (Statist. Methodology) 70(1):227–243.CrossrefGoogle Scholar
  • Deak I (1980) Three digit accurate multiple normal probabilities. Numerica Math. 35(4):369–380.CrossrefGoogle Scholar
  • Deak I (2003) Probabilities of simple n-dimensional sets for the normal distribution. IIE Trans. 35(3):285–293.CrossrefGoogle Scholar
  • Drezner Z (1990) Approximations to the multivariate normal integral. Commun. Statist. Simulation Comput. 19(2):527–534.CrossrefGoogle Scholar
  • Drezner Z (1992) Computation of the multivariate normal integral. ACM Trans. Math. Software 18(4):470–480.CrossrefGoogle Scholar
  • Gassmann HI, Deák I, Szántai T (2002) Computing multivariate normal probabilities: A new look. J. Comput. Graphical Statist. 11(4):920–949.CrossrefGoogle Scholar
  • Genz A (1992) Numerical computation of multivariate normal probabilities. J. Comput. Graphical Statist. 1(2):141–149.Google Scholar
  • Genz A (2004) Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Statist. Comput. 14(3):251–260.CrossrefGoogle Scholar
  • Genz A, Bretz F (2002) Comparison of methods for the computation of multivariate t probabilities. J. Comput. Graphical Statist. 11(4):950–971.CrossrefGoogle Scholar
  • Genz A, Bretz F (2009) Computation of Multivariate Normal and t Probabilities, vol 195 (Springer Science & Business Media, Berlin Heidelberg).CrossrefGoogle Scholar
  • Genz A, Kwong KS (2000) Numerical evaluation of singular multivariate normal distributions. J. Statist. Comput. Simulation 68(1):1–21.CrossrefGoogle Scholar
  • Geweke J (1991) Efficient simulation from the multivariate normal and student-t distributions subject to linear constraints and the evaluation of constraint probabilities. Comput. Sci. Statist. Proc. 23rd Sympos. Interface (Citeseer, Seattle), 571–578.Google Scholar
  • Gupta SS (1963) Probability integrals of multivariate normal and multivariate t. Ann. Math. Statist. 34(3):792–828.CrossrefGoogle Scholar
  • Hajivassiliou V, McFadden D, Ruud P (1996) Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results. J. Econom. 72(1):85–134.CrossrefGoogle Scholar
  • Henery R (1981) An approximation to certain multivariate normal probabilities. J. Royal Statist. Soc. Ser. B (Statist. Methodology) 43(1):81–85.Google Scholar
  • Joe H (1995) Approximations to multivariate normal rectangle probabilities based on conditional expectations. J. Amer. Statist. Assoc. 90(431):957–964.CrossrefGoogle Scholar
  • Lerman S, Manski C (1981) On the use of simulated frequencies to approximate choice probabilities. Structural Analysis of Discrete Data with Econometric Applications, vol 10 (MIT Press, Cambridge, MA), 305–319.Google Scholar
  • McFadden D (1989) A method of simulated moments for estimation of discrete response models without numerical integration. Econom. J. Econom. Soc. 57(5):995–1026.Google Scholar
  • Milton RC (1972) Computer evaluation of the multivariate normal integral. Technometrics 14(4):881–889.CrossrefGoogle Scholar
  • Miwa T, Hayter A, Kuriki S (2003) The evaluation of general non-centred orthant probabilities. J. Royal Statist. Soc. Ser. B (Statist. Methodology) 65(1):223–234.CrossrefGoogle Scholar
  • Morrison DF (1998) Multivariate Analysis, Overview (Wiley Online Library, Hoboken, NJ).Google Scholar
  • Nash JC (1990) Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation (CRC Press, Boca Raton, FL).Google Scholar
  • Nikoloulopoulos AK (2013) On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood. J. Statist. Planning Inference 143(11):1923–1937.CrossrefGoogle Scholar
  • Nikoloulopoulos AK (2016) Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses. Stochastic Environ. Res. Risk Assessment 30(2):493–505.CrossrefGoogle Scholar
  • Robert CP (2004) Monte Carlo Methods (Wiley Online Library, Hoboken, NJ).CrossrefGoogle Scholar
  • Schervish MJ (1984) Algorithm as 195: Multivariate normal probabilities with error bound. J. Royal Statist. Soc. Ser. C (Appl. Statist.) 33(1):81–94.Google Scholar
  • Šidák Z (1967) Rectangular confidence regions for the means of multivariate normal distributions. J. Amer. Statist. Assoc. 62(318):626–633.Google Scholar
  • Sidák Z (1968) On multivariate normal probabilities of rectangles: Their dependence on correlations. Ann. Math. Statist. 39(5):1425–1434.CrossrefGoogle Scholar
  • Slepian D (1962) The one-sided barrier problem for Gaussian noise. Bell Labs Tech. J. 41(2):463–501.CrossrefGoogle Scholar
  • Somerville PN (1998) Numerical computation of multivariate normal and multivariate-t probabilities over convex regions. J. Comput. Graphical Statist. 7(4):529–544.Google Scholar
  • Szántai T (2000) Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function. Ann. Oper. Res. 100(1–4):85–101.CrossrefGoogle Scholar
  • Tong YL (2012) The Multivariate Normal Distribution (Springer Science & Business Media, New York).Google Scholar
  • Vijverberg WP (1997) Monte Carlo evaluation of multivariate normal probabilities. J. Econom. 76(1):281–307.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.