IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v55y1995i1p131-142.html
   My bibliography  Save this article

Random record processes and state dependent thinning

Author

Listed:
  • Browne, Sid
  • Bunge, John

Abstract

Suppose that a point process , ... if [0, [infinity]) is thinned by independently retaining Tn with probability pn. Our main examples are the classical p-thinning (pn [reverse not equivalent] p) and the random record process (pn = 1/n). When is a mixed, nonhomogeneous Poisson process, we find conditions under which the thinned process is Poisson. When is a pure birth process (gamma-mixed Poisson with exponential rate), we show that the record process is Markov renewal, with an interesting structure, and we compare this with related asymptotic results. When is a Mittag-Leffler renewal process (the homogeneous Poisson is a special case), we give a "Deheuvels-type" representation of the record process (Deheuvels, 1982) and related characterization results.

Suggested Citation

  • Browne, Sid & Bunge, John, 1995. "Random record processes and state dependent thinning," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 131-142, January.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:1:p:131-142
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)00022-L
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Steutel, F. W., 1973. "Some recent results in infinite divisibility," Stochastic Processes and their Applications, Elsevier, vol. 1(2), pages 125-143, April.
    2. 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.
    3. 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.
    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.
    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. Gnedin, Alexander, 2022. "The best choice problem with random arrivals: How to beat the 1/e-strategy," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 226-240.

    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. Vanessa Didelez, 2008. "Graphical models for marked point processes based on local independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 245-264, February.
    2. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    3. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    4. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.
    5. Emad-Eldin Aly & Nadjib Bouzar, 2000. "On Geometric Infinite Divisibility and Stability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 790-799, December.
    6. Lennart Bondesson, 2015. "A Class of Probability Distributions that is Closed with Respect to Addition as Well as Multiplication of Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1063-1081, September.
    7. Levy, Edmond, 2021. "On the density for sums of independent Mittag-Leffler variates with common order," Statistics & Probability Letters, Elsevier, vol. 179(C).
    8. Subrata Chakraborty & S. H. Ong, 2017. "Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    9. Kozubowski, Tomasz J., 2005. "A note on self-decomposability of stable process subordinated to self-decomposable subordinator," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 89-91, August.
    10. Gadi Barlevy, 2003. "Estimating models of on-the-job search using record statistics," Working Paper Series WP-03-18, Federal Reserve Bank of Chicago.
    11. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).
    12. K. K. Kataria & P. Vellaisamy, 2019. "On Distributions of Certain State-Dependent Fractional Point Processes," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1554-1580, September.
    13. Cirillo, Pasquale & Hüsler, Jürg, 2009. "An urn approach to generalized extreme shock models," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 969-976, April.
    14. Erhan Bayraktar & Michael Ludkovski, 2010. "Inventory management with partially observed nonstationary demand," Annals of Operations Research, Springer, vol. 176(1), pages 7-39, April.
    15. Barlevy, Gadi & Nagaraja, H. N., 2006. "Identification of Search Models with Initial Condition Problems," IZA Discussion Papers 2061, Institute of Labor Economics (IZA).
    16. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
    17. Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
    18. Sánchez, Ewin, 2019. "Burr type-XII as a superstatistical stationary distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 443-446.
    19. Calatayud, Julia & Jornet, Marc & Pinto, Carla M.A., 2024. "On the interpretation of Caputo fractional compartmental models," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    20. Jin Feng, 2002. "A Stochastic Filtering Approach To Survival Analysis," Statistical Inference for Stochastic Processes, Springer, vol. 5(1), pages 23-53, January.

    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:eee:spapps:v:55:y:1995:i:1:p:131-142. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.