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

Author

Listed:
  • Jietao Xie

    (Baicheng Ordnance Test Center of China, Baicheng 137001, Jilin, China)

  • Juan Wu

    (Baicheng Ordnance Test Center of China, Baicheng 137001, Jilin, China)

Abstract

The consecutive hit probability of antiaircraft artillery corresponds to the multivariate normal probability distribution. The computational complexity depends on the length of the firing error sequence (i.e., the integral dimension may exceed 100). The traditional numerical integration and the Monte Carlo method are too slow for this calculation. This paper established the state equation of the firing error sequence, which was the bridge between the multivariate normal probability distribution and stochastic process theory. The recursive calculation model was given after the rigorous derivation process. The accuracy and computational complexity of the model were quantified by theoretical analysis and expressed intuitively by examples. The model shows the upper bound for the absolute error, and the computational efficiency is significantly improved.

Suggested Citation

  • Jietao Xie & Juan Wu, 2020. "Recursive Calculation Model for a Special Multivariate Normal Probability of First-Order Stationary Sequence," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 164-171, January.
    • Handle: RePEc:inm:orijoc:v:32:y:2020:i:1:p:164-171
    DOI: 10.1287/ijoc.2018.0852
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    References listed on IDEAS

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    1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    2. Mark J. Schervish, 1984. "Multivariate Normal Probabilities with Error Bound," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 81-94, March.
    3. Peter Craig, 2008. "A new reconstruction of multivariate normal orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 227-243, February.
    4. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
    5. Tetsuhisa Miwa & A. J. Hayter & Satoshi Kuriki, 2003. "The evaluation of general non‐centred orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 223-234, February.
    6. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
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