IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v180y2022ics0167715221002054.html
   My bibliography  Save this article

Identification of parameters from the distribution of the maximum or minimum of Poisson random variables

Author

Listed:
  • Kim, Bara
  • Kim, Jeongsim

Abstract

Bi and Mukherjea (2011) considered the following problem: If X1,…,Xn are independent Poisson distributed random variables with parameters λ1,…,λn, respectively, then does the distribution of max{X1,…,Xn} or of min{X1,…,Xn} uniquely determine the parameters? They proved that the distribution of max{X1,X2,X3} uniquely determines λ1,λ2 and λ3. In this paper, we prove the identifiability problem of parameters from the distribution of max{X1,…,Xn} or of min{X1,…,Xn} for any value of n.

Suggested Citation

  • Kim, Bara & Kim, Jeongsim, 2022. "Identification of parameters from the distribution of the maximum or minimum of Poisson random variables," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221002054
    DOI: 10.1016/j.spl.2021.109243
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221002054
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109243?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. Bi, L. & Mukherjea, A., 2011. "Poisson distributions: Identification of parameters from the distribution of the maximum and a conjecture on the partial sums of the power series for exp(x)," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 611-613, May.
    2. Mukherjea, A. & Nakassis, A. & Miyashita, J., 1986. "The problem of identification of parameters by the distribution of the maximum random variable," Journal of Multivariate Analysis, Elsevier, vol. 18(2), pages 178-186, April.
    3. Davis, J. & Mukherjea, A., 2007. "Identification of parameters by the distribution of the minimum: The tri-variate normal case with negative correlations," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1141-1159, July.
    4. Basu, A. P. & Ghosh, J. K., 1978. "Identifiability of the multinormal and other distributions under competing risks model," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 413-429, September.
    5. Mukherjea, Arunava & Stephens, Richard, 1990. "The problem of identification of parameters by the distribution of the maximum random variable: Solution for the trivariate normal case," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 95-115, July.
    Full references (including those not matched with items on IDEAS)

    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. Irene Hueter, 2000. "Recovering a Family of Two-Dimensional Gaussian Variables from the Minimum Process," Journal of Theoretical Probability, Springer, vol. 13(4), pages 939-950, October.
    2. Bi, L. & Mukherjea, A., 2010. "Identification of parameters and the distribution of the minimum of the tri-variate normal," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1819-1826, December.
    3. Ming Dai & Arunava Mukherjea, 2001. "Identification of the Parameters of a Multivariate Normal Vector by the Distribution of the Maximum," Journal of Theoretical Probability, Springer, vol. 14(1), pages 267-298, January.
    4. Bi, L. & Mukherjea, A., 2011. "Poisson distributions: Identification of parameters from the distribution of the maximum and a conjecture on the partial sums of the power series for exp(x)," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 611-613, May.
    5. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    6. Schwarz, Maik & Jongbloed, Geurt & Van Keilegom, Ingrid, 2012. "On the identifiability of copulas in bivariate competing risks models," LIDAM Discussion Papers ISBA 2012032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 673-682, December.
    8. Elliot Anenberg & Aurel Hizmo & Edward Kung & Raven Molloy, 2019. "Measuring mortgage credit availability: A frontier estimation approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 865-882, September.
    9. Deresa, Negera Wakgari & Van Keilegom, Ingrid, 2020. "A multivariate normal regression model for survival data subject to different types of dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Casey Rothschild & Florian Scheuer, 2013. "Redistributive Taxation in the Roy Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 623-668.
    11. Bunea, Cornel & Mazzuchi, Thomas A. & Sarkani, Shahram & Chang, Hai-Chin, 2008. "Application of modern reliability database techniques to military system data," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 14-27.
    12. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    13. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.
    14. Disney, Stephen M. & Gaalman, Gerard J.C. & Hedenstierna, Carl Philip T. & Hosoda, Takamichi, 2015. "Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 501-512.
    15. Jamalizadeh, A. & Balakrishnan, N., 2009. "Prediction in a trivariate normal distribution via a linear combination of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2289-2296, November.
    16. Enkelejd Hashorva, 2005. "Asymptotics and Bounds for Multivariate Gaussian Tails," Journal of Theoretical Probability, Springer, vol. 18(1), pages 79-97, January.
    17. R. Arellano-Valle & Ahad Jamalizadeh & H. Mahmoodian & N. Balakrishnan, 2014. "$$L$$ L -statistics from multivariate unified skew-elliptical distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 559-583, May.
    18. Roohollah Roozegar & Ahad Jamalizadeh & Mehdi Amiri & Tsung-I Lin, 2018. "On the exact distribution of order statistics arising from a doubly truncated bivariate elliptical distribution," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 99-114, April.
    19. Jia-Han Shih & Takeshi Emura, 2019. "Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula," Statistical Papers, Springer, vol. 60(4), pages 1101-1118, August.
    20. Ruixuan Liu, 2020. "A competing risks model with time‐varying heterogeneity and simultaneous failure," Quantitative Economics, Econometric Society, vol. 11(2), pages 535-577, May.

    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:180:y:2022:i:c:s0167715221002054. 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.