IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v56y2015i2p453-477.html
   My bibliography  Save this article

Improved estimators of the distribution function based on lower record values

Author

Listed:
  • R. Arabi Belaghi
  • M. Arashi
  • S. Tabatabaey

Abstract

In this paper, we define different types of estimators for the distribution function, namely preliminary test (PT), shrinkage PT (SPT), Stein type (S), and Thompson shrinkage (TS) estimators based on lower record observations and their inter record times. Their asymptotic distributional bias and mean square error are explicitly derived. The superiority conditions of the new proposed estimators over the existing estimator of distribution function are also obtained. It is shown that about the neighborhood of the null hypothesis $$F_0$$ F 0 , the PTE is superior to the SE in the sense of having higher asymptotic relative efficiency. Further for the reasonable values of $$\alpha $$ α the newly proposed SPT estimator uniformly dominates the non-parametric maximum like likelihood estimators in the literatures. A table is also given to be more specifics along the exhibited theoretical results for practical sake. Some graphical representations are given as proofs of our assertions. A simulation study is also carried out for some life time distribution, to examine the accuracy of the proposed estimators with a limited sample size. The results show that combination of the parametric and nonparametric estimators will give more efficient estimators. This study is finally concluded by applying the theoretic results to a real data set. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2015. "Improved estimators of the distribution function based on lower record values," Statistical Papers, Springer, vol. 56(2), pages 453-477, May.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:2:p:453-477
    DOI: 10.1007/s00362-014-0591-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-014-0591-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-014-0591-9?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. Balakrishnan, N. & Stepanov, A., 2006. "On the Fisher information in record data," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 537-545, March.
    2. J. Ravichandran, 2012. "A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners," Statistical Papers, Springer, vol. 53(3), pages 531-547, August.
    3. Jafar Ahmadi & N. Balakrishnan, 2013. "On the nearness of record values to order statistics from Pitman’s measure of closeness," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 521-541, May.
    4. B. Kibria & A. Saleh, 2010. "Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples," Statistical Papers, Springer, vol. 51(4), pages 757-773, December.
    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. A. Asgharzadeh & S. F. Bagheri & N. A. Ibrahim & M. R. Abubakar, 2020. "Optimal confidence regions for the two-parameter exponential distribution based on records," Computational Statistics, Springer, vol. 35(1), pages 309-326, March.
    2. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.

    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. Park, Jeong-Soo & Yoon Kim, Tae, 2007. "Fisher information matrix for a four-parameter kappa distribution," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1459-1466, July.
    2. Pakhteev, A. & Stepanov, A., 2016. "Simulation of Gamma records," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 204-212.
    3. R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    4. R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2014. "Improved confidence intervals for the scale parameter of Burr XII model based on record values," Computational Statistics, Springer, vol. 29(5), pages 1153-1173, October.
    5. S. MirMostafaee & Jafar Ahmadi & Narjes Sadeghian, 2015. "Pitman closeness of predictors of future order statistics for two parameter exponential distribution," Computational Statistics, Springer, vol. 30(4), pages 1163-1183, December.

    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:stpapr:v:56:y:2015:i:2:p:453-477. 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.