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Asymptotic analysis of simultaneous damages in spatial Boolean models

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  • Haijun Li
  • Susan Xu
  • Way Kuo

Abstract

A notion of the positive spatial association is introduced in this paper to analyze spatial dependence of Boolean models with the focus on estimating the long-range spatial dependence. The explicit tail estimates for probabilities of simultaneous damage to two distant spatial regions are obtained using the regular variation method, and the long-range spatial covariance for the Boolean models with heavy-tailed grains is shown to decay at the power-law rate that is smaller than the tail decay rate of grains. Examples and applications to spatial reliability modeling are also discussed. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Haijun Li & Susan Xu & Way Kuo, 2014. "Asymptotic analysis of simultaneous damages in spatial Boolean models," Annals of Operations Research, Springer, vol. 212(1), pages 139-154, January.
    • Handle: RePEc:spr:annopr:v:212:y:2014:i:1:p:139-154:10.1007/s10479-013-1363-y
    DOI: 10.1007/s10479-013-1363-y
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    References listed on IDEAS

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    1. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    2. Hwang, Jung Yoon & Kuo, Way, 2007. "Model-based clustering for integrated circuit yield enhancement," European Journal of Operational Research, Elsevier, vol. 178(1), pages 143-153, April.
    3. Vladik Kreinovich & Monchaya Chiangpradit & Wararit Panichkitkosolkul, 2012. "Efficient algorithms for heavy-tail analysis under interval uncertainty," Annals of Operations Research, Springer, vol. 195(1), pages 73-96, May.
    4. Zhu, Li & Li, Haijun, 2012. "Tail distortion risk and its asymptotic analysis," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 115-121.
    5. Li, Haijun, 2003. "Association of multivariate phase-type distributions, with applications to shock models," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 381-392, October.
    6. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
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    Cited by:

    1. Olufolajimi Oke & Kavi Bhalla & David C. Love & Sauleh Siddiqui, 2018. "Spatial associations in global household bicycle ownership," Annals of Operations Research, Springer, vol. 263(1), pages 529-549, April.

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