IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v131y2014icp216-227.html
   My bibliography  Save this article

Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study

Author

Listed:
  • Musleh, Rola M.
  • Helu, Amal

Abstract

In this article we consider statistical inferences about the unknown parameters of the Inverse Weibull distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures we propose using the maximum likelihood; the least squares methods and the approximate maximum likelihood estimators. The Bayes estimators are obtained based on both the symmetric and asymmetric (Linex, General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators, therefore, we propose Lindley׳s approximation method to compute the Bayes estimators. A comparison between these estimators is provided by using extensive simulation and three criteria, namely, Bias, mean squared error and Pitman nearness (PN) probability. It is concluded that the approximate Bayes estimators outperform the classical estimators most of the time. Real life data example is provided to illustrate our proposed estimators.

Suggested Citation

  • Musleh, Rola M. & Helu, Amal, 2014. "Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 216-227.
    • Handle: RePEc:eee:reensy:v:131:y:2014:i:c:p:216-227
    DOI: 10.1016/j.ress.2014.07.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014001616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.07.006?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. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    2. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    3. N. Balakrishnan, 2007. "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 211-259, August.
    4. Mahmoud, M. A. W. & Sultan, K. S. & Amer, S. M., 2003. "Order statistics from inverse weibull distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 149-163, February.
    5. N. Balakrishnan, 2007. "Rejoinder 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 290-296, August.
    6. Chansoo Kim & Keunhee Han, 2010. "Estimation of the scale parameter of the half-logistic distribution under progressively type II censored sample," Statistical Papers, Springer, vol. 51(2), pages 375-387, June.
    7. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
    8. Mohamed Abdel Wahab Mahmoud & Khalaf Salman Sultan & Safaa Mousa Amer, 2003. "Order statistics from inverse Weibull distribution and characterizations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 389-401.
    9. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    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. Altındağ, Ömer & Aydoğdu, Halil, 2021. "Estimation of renewal function under progressively censored data and its applications," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Xinjing Wang & Wenhao Gui, 2021. "Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    3. Leonardo Leoni & Farshad BahooToroody & Saeed Khalaj & Filippo De Carlo & Ahmad BahooToroody & Mohammad Mahdi Abaei, 2021. "Bayesian Estimation for Reliability Engineering: Addressing the Influence of Prior Choice," IJERPH, MDPI, vol. 18(7), pages 1-16, March.
    4. Jia, Xiang & Wang, Dong & Jiang, Ping & Guo, Bo, 2016. "Inference on the reliability of Weibull distribution with multiply Type-I censored data," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 171-181.
    5. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    6. Franko, Mitja & Nagode, Marko, 2015. "Probability density function of the equivalent stress amplitude using statistical transformation," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 118-125.
    7. Sarah R. Al-Dawsari & Khalaf S. Sultan, 2021. "Inverted Weibull Regression Models and Their Applications," Stats, MDPI, vol. 4(2), pages 1-22, April.

    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. Manoj Kumar Rastogi & Yogesh Mani Tripathi, 2014. "Estimation for an inverted exponentiated Rayleigh distribution under type II progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2375-2405, November.
    2. Balakrishnan, N. & Saleh, H.M., 2011. "Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2775-2792, October.
    3. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    4. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    5. Kousik Maiti & Suchandan Kayal, 2023. "Estimating Reliability Characteristics of the Log-Logistic Distribution Under Progressive Censoring with Two Applications," Annals of Data Science, Springer, vol. 10(1), pages 89-128, February.
    6. Teena Goyal & Piyush K. Rai & Sandeep K. Maurya, 2020. "Bayesian Estimation for GDUS Exponential Distribution Under Type-I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 7(2), pages 307-345, June.
    7. Sarah R. Al-Dawsari & Khalaf S. Sultan, 2021. "Inverted Weibull Regression Models and Their Applications," Stats, MDPI, vol. 4(2), pages 1-22, April.
    8. Abdullah Fathi & Al-Wageh A. Farghal & Ahmed A. Soliman, 2022. "Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    9. Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Abd-Elmougod, Gamal A., 2012. "Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2471-2485.
    10. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    11. Sukhdev Singh & Yogesh Mani Tripathi, 2018. "Estimating the parameters of an inverse Weibull distribution under progressive type-I interval censoring," Statistical Papers, Springer, vol. 59(1), pages 21-56, March.
    12. Mazen Nassar & Refah Alotaibi & Ahmed Elshahhat, 2023. "Reliability Estimation of XLindley Constant-Stress Partially Accelerated Life Tests using Progressively Censored Samples," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    13. Park, Sangun & Ng, Hon Keung Tony & Chan, Ping Shing, 2015. "On the Fisher information and design of a flexible progressive censored experiment," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 142-149.
    14. Rui Hua & Wenhao Gui, 2022. "Revisit to progressively Type-II censored competing risks data from Lomax distributions," Journal of Risk and Reliability, , vol. 236(3), pages 377-394, June.
    15. Olayan Albalawi & Naresh Chandra Kabdwal & Qazi J. Azhad & Rashi Hora & Basim S. O. Alsaedi, 2022. "Estimation of the Generalized Logarithmic Transformation Exponential Distribution under Progressively Type-II Censored Data with Application to the COVID-19 Mortality Rates," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    16. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    17. Wu, Shuo-Jye & Huang, Syuan-Rong, 2017. "Planning two or more level constant-stress accelerated life tests with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 1-8.
    18. Bander Al-Zahrani & Areej M. AL-Zaydi, 2022. "Moments of progressively type-II censored order statistics from the complementary exponential geometric distribution and associated inference," 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. 13(3), pages 1052-1065, June.
    19. E. M. Almetwally & H. M. Almongy & M. K. Rastogi & M. Ibrahim, 2020. "Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes," Annals of Data Science, Springer, vol. 7(2), pages 257-279, June.
    20. Xiaojun Zhu & N. Balakrishnan & Helton Saulo, 2019. "On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 759-778, October.

    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:reensy:v:131:y:2014:i:c:p:216-227. 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: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.