IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i2p135-143.html
   My bibliography  Save this article

On the expectation of the maximum of IID geometric random variables

Author

Listed:
  • Eisenberg, Bennett

Abstract

A study of the expected value of the maximum of independent, identically distributed (IID) geometric random variables is presented based on the Fourier analysis of the distribution of the fractional part of the maximum of corresponding IID exponential random variables.

Suggested Citation

  • Eisenberg, Bennett, 2008. "On the expectation of the maximum of IID geometric random variables," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 135-143, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:135-143
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00204-0
    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. Baryshnikov, Yuliy & Eisenberg, Bennett & Stengle, Gilbert, 1995. "A necessary and sufficient condition for the existence of the limiting probability of a tie for first place," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 203-209, May.
    2. Brands, J. J. A. M. & Steutel, F. W. & Wilms, R. J. G., 1994. "On the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 209-217, June.
    3. Jeske, Daniel R. & Blessinger, Todd, 2004. "Tunable Approximations for the Mean and Variance of the Maximum of Heterogeneous Geometrically Distributed Random Variables," The American Statistician, American Statistical Association, vol. 58, pages 322-327, November.
    4. Olofsson, Peter, 1999. "A Poisson approximation with applications to the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 23-27, August.
    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. Yakubovich, Yu., 2015. "On descents after maximal values in samples of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 203-208.
    2. Fontes, Luiz Renato & Schinazi, Rinaldo B., 2019. "Implosion of a pure death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1171-1174.
    3. Thierry E. Huillet, 2019. "Partitioning Problems Arising From Independent Shifted-Geometric and Exponential Samples With Unequal Intensities," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-31, November.

    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. Archibald, Margaret & Knopfmacher, Arnold, 2009. "The average position of the dth maximum in a sample of geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 864-872, April.
    2. Eisenberg, Bennett, 2009. "The number of players tied for the record," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 283-288, February.
    3. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
    4. Qi, Y. & Wilms, R. J. G., 1997. "The limit behavior of maxima modulo one and the number of maxima," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 75-84, May.
    5. Qi, Yongcheng, 1997. "A note on the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 373-377, May.
    6. Qi, Yongcheng & Wilms, R. J. G., 1997. "The limit behavior of maxima modulo one and the number of maxima," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 357-366, April.
    7. Jasiński, Krzysztof, 2016. "Asymptotic normality of numbers of observations near order statistics from stationary processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 259-263.
    8. Peng Zhao & Feng Su, 2014. "On maximum order statistics from heterogeneous geometric variables," Annals of Operations Research, Springer, vol. 212(1), pages 215-223, January.
    9. Athreya, J. S. & Sethuraman, S., 2001. "On the asymptotics of discrete order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 243-249, October.
    10. Olofsson, Peter, 1999. "A Poisson approximation with applications to the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 23-27, August.
    11. Arvydas Astrauskas, 2023. "Some Bounds for the Expectations of Functions on Order Statistics and Their Applications," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1116-1147, June.
    12. Archibald, Margaret & Blecher, Aubrey & Brennan, Charlotte & Knopfmacher, Arnold & Prodinger, Helmut, 2017. "Geometric random variables: Descents following maxima," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 140-147.
    13. Baryshnikov, Yuliy & Eisenberg, Bennett & Stengle, Gilbert, 1995. "A necessary and sufficient condition for the existence of the limiting probability of a tie for first place," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 203-209, May.
    14. Yakubovich, Yu., 2015. "On descents after maximal values in samples of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 203-208.
    15. Nevzorov, Valery B. & Stepanov, Alexei, 2024. "On uppermost discrete spacing," Statistics & Probability Letters, Elsevier, vol. 208(C).
    16. Anna Dembińska, 2017. "An ergodic theorem for proportions of observations that fall into random sets determined by sample quantiles," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 319-332, April.
    17. Archibald, Margaret & Blecher, Aubrey & Brennan, Charlotte & Knopfmacher, Arnold, 2015. "Descents following maximal values in samples of geometric random variables," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 229-240.
    18. Khmaladze, E. & Nadareishvili, M. & Nikabadze, A., 1997. "Asymptotic behaviour of a number of repeated records," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 49-58, August.
    19. Lin, Jin-Guan & Huang, Chao & Zhuang, Qing-Yun & Zhu, Li-Ping, 2010. "Estimating generalized state density of near-extreme events and its applications in analyzing stock data," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 13-20, August.

    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:stapro:v:78:y:2008:i:2:p:135-143. 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/622892/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.