IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v68y2004i1p83-90.html
   My bibliography  Save this article

Logconcavity and unimodality of progressively censored order statistics

Author

Listed:
  • Cramer, Erhard

Abstract

Logconcavity and unimodality properties of the distribution of progressively censored order statistics are established and applications to aging notions are presented. Some extensions to generalized order statistics are discussed.

Suggested Citation

  • Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:1:p:83-90
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00072-0
    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. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    2. Aliev, Fazil Alioglu, 2003. "A comment on 'Unimodality of the distribution of record statistics'," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 39-40, August.
    3. Basak, Prasanta & Basak, Indrani, 2002. "Unimodality of the distribution of record statistics," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 395-398, February.
    4. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    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. Jorge Navarro & Marco Burkschat, 2011. "Coherent systems based on sequential order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 123-135, March.
    2. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein, 2011. "Some new results on unimodality of generalized order statistics and their spacings," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1677-1682, November.
    3. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein & Cramer, Erhard, 2015. "Discrete strong unimodality of order statistics," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 176-185.
    4. Mahdi Alimohammadi & Mohammad Hossein Alamatsaz & Erhard Cramer, 2016. "Convolutions and generalization of logconcavity: Implications and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 109-123, March.
    5. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    6. Chen, Huaihou & Xie, Hongmei & Hu, Taizhong, 2009. "Log-concavity of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 396-399, February.

    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. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein, 2011. "Some new results on unimodality of generalized order statistics and their spacings," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1677-1682, November.
    2. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein & Cramer, Erhard, 2015. "Discrete strong unimodality of order statistics," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 176-185.
    3. Hashemi, Marzieh & Tavangar, Mahdi & Asadi, Majid, 2010. "Some properties of the residual lifetime of progressively Type-II right censored order statistics," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 848-859, May.
    4. Udo Kamps & Erhard Cramer, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 271-275, August.
    5. Hu, Taizhong & Zhuang, Weiwei, 2005. "A note on stochastic comparisons of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 163-170, April.
    6. Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    7. N. Balakrishnan & Erhard Cramer, 2008. "Progressive censoring from heterogeneous distributions with applications to robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 151-171, March.
    8. Tomasz Rychlik, 2010. "Evaluations of generalized order statistics from bounded populations," Statistical Papers, Springer, vol. 51(1), pages 165-177, January.
    9. Mahdi Alimohammadi & Mohammad Hossein Alamatsaz & Erhard Cramer, 2016. "Convolutions and generalization of logconcavity: Implications and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 109-123, March.
    10. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    11. M. Hermanns & E. Cramer, 2018. "Inference with progressively censored k-out-of-n system lifetime data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 787-810, December.
    12. Manoj Kumar & Anurag Pathak & Sukriti Soni, 2019. "Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal," Annals of Data Science, Springer, vol. 6(1), pages 117-152, March.
    13. Yashi Wang & Weiwei Zhuang & Taizhong Hu, 2010. "Conditionally stochastic domination of generalized order statistics from two samples," Statistical Papers, Springer, vol. 51(2), pages 369-373, June.
    14. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    15. Vuong, Q.N. & Bedbur, S. & Kamps, U., 2013. "Distances between models of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 24-36.
    16. Beutner, E. & Cramer, E., 2014. "Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 95-109.
    17. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    18. Burkschat, M., 2009. "Multivariate dependence of spacings of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1093-1106, July.
    19. Morteza Amini & Narayanaswamy Balakrishnan, 2015. "Pooled parametric inference for minimal repair systems," Computational Statistics, Springer, vol. 30(2), pages 605-623, June.
    20. Mariusz Bieniek & Krystyna Macia̧g, 2018. "Uniqueness of characterization of absolutely continuous distributions by regressions of generalized order statistics," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 359-380, July.

    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:68:y:2004:i:1:p:83-90. 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.