IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v11y2002i2d10.1007_bf02511486.html
   My bibliography  Save this article

Computing maximum likelihood estimates from type II doubly censored exponential data

Author

Listed:
  • Arturo J. fernández

    (Universidad de La Laguna)

  • José I. Bravo

    (Universidad de La Laguna)

  • Íñigo Fuentes

    (Universidad de La Laguna)

Abstract

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.

Suggested Citation

  • Arturo J. fernández & José I. Bravo & Íñigo Fuentes, 2002. "Computing maximum likelihood estimates from type II doubly censored exponential data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(2), pages 187-200, June.
  • Handle: RePEc:spr:stmapp:v:11:y:2002:i:2:d:10.1007_bf02511486
    DOI: 10.1007/BF02511486
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/BF02511486
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/BF02511486?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. Elfessi, Abdulaziz, 1997. "Estimation of a linear function of the parameters of an exponential distribution from doubly censored samples," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 251-259, 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. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    2. Carlos Pérez-González & Arturo Fernández, 2009. "Accuracy of approximate progressively censored reliability sampling plans for exponential models," Statistical Papers, Springer, vol. 50(1), pages 161-170, January.
    3. Fernández, Arturo J., 2008. "Reliability inference and sample-size determination under double censoring for some two-parameter models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3426-3440, March.
    4. Fernandez, Arturo J., 2006. "Bayesian estimation based on trimmed samples from Pareto populations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1119-1130, November.
    5. Fernandez, Arturo J., 2006. "Bounding maximum likelihood estimates based on incomplete ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2014-2027, April.
    6. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.

    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. T. Madi, Mohamed, 2002. "On the invariant estimation of an exponential scale using doubly censored data," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 77-82, January.
    2. Madi, Mohamed T., 2008. "Improved estimation of an exponential scale ratio based on records," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 165-172, February.
    3. Constantinos Petropoulos & Stavros Kourouklis, 2001. "Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 746-759, 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:stmapp:v:11:y:2002:i:2:d:10.1007_bf02511486. 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.