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The multivariate hazard construction

Author

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  • Shaked, Moshe
  • George Shanthikumar, J.

Abstract

A representation, called the total hazard construction, of dependent random variables by means of independent exponential random variables is studied. Conditions which imply association of nonnegative random variables are found using this construction. Furthermore, new conditions which imply stochastic ordering between two nonnegative random vectors are obtained. These strengthen previous results of the authors. Further applications in reliability theory and in simulation are indicated.

Suggested Citation

  • Shaked, Moshe & George Shanthikumar, J., 1987. "The multivariate hazard construction," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 241-258, May.
  • Handle: RePEc:eee:spapps:v:24:y:1987:i:2:p:241-258
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    References listed on IDEAS

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    1. Bruss, F. T. & Rogers, L. C. G., 1991. "Pascal processes and their characterization," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 331-338, April.
    2. Steutel, F. W., 1973. "Some recent results in infinite divisibility," Stochastic Processes and their Applications, Elsevier, vol. 1(2), pages 125-143, April.
    3. Arjas, Elja & Haara, Pentti & Norros, Ikka, 1992. "Filtering the histories of a partially observed marked point process," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 225-250, March.
    4. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    5. Böker, Fred & Serfozo, Richard, 1983. "Ordered thinnings of point processes and random measures," Stochastic Processes and their Applications, Elsevier, vol. 15(2), pages 113-132, July.
    6. Bunge, J. A. & Nagaraja, H. N., 1991. "The distributions of certain record statistics from a random number of observations," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 167-183, June.
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    Citations

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    Cited by:

    1. Yinghui Dong & Xue Liang & Guojing Wang, 2012. "Unilateral Counterparty Risk Valuation for CDS Under a Regime Switching Interacting Intensities Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(4), pages 391-415, November.
    2. Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1999. "Dynamic Linkages for Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 54-77, January.
    3. Harry Zheng & Lishang Jiang, 2009. "Basket CDS pricing with interacting intensities," Finance and Stochastics, Springer, vol. 13(3), pages 445-469, September.
    4. Damiano Brigo & Jan-Frederik Mai & Matthias Scherer, 2013. "Consistent iterated simulation of multi-variate default times: a Markovian indicators characterization," Papers 1306.0887, arXiv.org, revised May 2014.
    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. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2013. "On pricing basket credit default swaps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1845-1854, December.
    7. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2014. "On reduced-form intensity-based model with ‘trigger’ events," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(3), pages 331-339, March.
    8. Dong, Yinghui & Yuen, Kam C. & Wu, Chongfeng, 2014. "Unilateral counterparty risk valuation of CDS using a regime-switching intensity model," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 25-35.
    9. repec:eee:ejores:v:264:y:2018:i:1:p:340-353 is not listed on IDEAS
    10. Dong, Yinghui & Wang, Guojing, 2014. "Bilateral counterparty risk valuation for credit default swap in a contagion model using Markov chain," Economic Modelling, Elsevier, vol. 40(C), pages 91-100.
    11. Feng-Hui Yu & Wai-Ki Ching & Jia-Wen Gu & Tak-Kuen Siu, 2016. "Interacting Default Intensity with Hidden Markov Process," Papers 1603.02902, arXiv.org.

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