IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v3y2001i4d10.1023_a1015412103008.html
   My bibliography  Save this article

Directionally Convex Comparison of Correlated First Passage Times

Author

Listed:
  • Haijun Li

    (Washington State University)

  • Susan H. Xu

    (Pennsylvania State University)

Abstract

Many important classes of multivariate distributions arising from reliability modeling are the distributions of correlated first passage times of certain multivariate point processes. In this paper, we obtain results that compare variability and dependence structure of these correlated first passage times, in the sense of directionally convex ordering. Under certain conditions, we also obtain some easily computable distributional bounds for the first passage times whose joint distributions can not be expressed explicitly.

Suggested Citation

  • Haijun Li & Susan H. Xu, 2001. "Directionally Convex Comparison of Correlated First Passage Times," Methodology and Computing in Applied Probability, Springer, vol. 3(4), pages 365-378, December.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:4:d:10.1023_a:1015412103008
    DOI: 10.1023/A:1015412103008
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1015412103008
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1015412103008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pellerey, Franco, 1999. "Stochastic Comparisons for Multivariate Shock Models," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 42-55, October.
    2. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 509-531, September.
    3. Susan H. Xu & Haijun Li, 2000. "Majorization of Weighted Trees: A New Tool to Study Correlated Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 298-323, May.
    4. V. G. Kulkarni, 1989. "A New Class of Multivariate Phase Type Distributions," Operations Research, INFORMS, vol. 37(1), pages 151-158, February.
    5. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    6. David Assaf & Naftali A. Langberg & Thomas H. Savits & Moshe Shaked, 1984. "Multivariate Phase-Type Distributions," Operations Research, INFORMS, vol. 32(3), pages 688-702, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kulik, Rafal & Szekli, Ryszard, 2005. "Dependence orderings for some functionals of multivariate point processes," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 145-173, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Michel Denuit & Esther Frostig & Benny Levikson, 2007. "Supermodular Comparison of Time-to-Ruin Random Vectors," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 41-54, March.
    3. Qi-Ming He & Jiandong Ren, 2016. "Analysis of a Multivariate Claim Process," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 257-273, March.
    4. Surya, Budhi Arta, 2022. "Conditional multivariate distributions of phase-type for a finite mixture of Markov jump processes given observations of sample path," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    5. Bo Friis Nielsen, 2022. "Characterisation of multivariate phase type distributions," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 229-231, April.
    6. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    7. Woo, Jae-Kyung, 2016. "On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 354-363.
    8. Fierro, Raúl & Leiva, Víctor & Maidana, Jean Paul, 2018. "Cumulative damage and times of occurrence for a multicomponent system: A discrete time approach," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 323-333.
    9. Kulik, Rafal & Szekli, Ryszard, 2005. "Dependence orderings for some functionals of multivariate point processes," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 145-173, January.
    10. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.
    11. J. M. Fernández-Ponce & M. R. Rodríguez-Griñolo, 2017. "New properties of the orthant convex-type stochastic orders," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 618-637, September.
    12. Berdel, Jasmin & Hipp, Christian, 2011. "Convolutions of multivariate phase-type distributions," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 374-377, May.
    13. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    14. Qi-Ming He & Jiandong Ren, 2016. "Parameter Estimation of Discrete Multivariate Phase-Type Distributions," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 629-651, September.
    15. Masih-Tehrani, Behdad & Xu, Susan H. & Kumara, Soundar & Li, Haijun, 2011. "A single-period analysis of a two-echelon inventory system with dependent supply uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1128-1151, September.
    16. Ren Jiandong & Zitikis Ricardas, 2017. "CMPH: a multivariate phase-type aggregate loss distribution," Dependence Modeling, De Gruyter, vol. 5(1), pages 304-315, December.
    17. Cai, Jun & Li, Haijun, 2007. "Dependence properties and bounds for ruin probabilities in multivariate compound risk models," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 757-773, April.
    18. Laureano Escudero & Eva-María Ortega, 2009. "How retention levels influence the variability of the total risk under reinsurance," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 139-157, July.
    19. Shaked, Moshe, 2007. "Stochastic comparisons of multivariate random sums in the Laplace transform order, with applications," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1339-1344, July.
    20. Eisele, Karl-Theodor, 2008. "Recursions for multivariate compound phase variables," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 65-72, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:3:y:2001:i:4:d:10.1023_a:1015412103008. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.