IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v40y2013i7p1464-1479.html
   My bibliography  Save this article

Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data

Author

Listed:
  • Conghua Cheng
  • Jinyuan Chen
  • Jianming Bai

Abstract

We develop an exact inference for the location and the scale parameters of the two-exponential distribution and the Pareto distribution based on their maximum-likelihood estimators from the doubly Type-II and the progressive Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. We also provide a bootstrap method for constructing a confidence interval. Some simulation studies are carried out to assess their performances. Using the exact distribution of the scale parameter, we establish an acceptance sampling procedure based on the lifetime of the unit. Some numerical results are tabulated for the illustration. One biometrical example is also given to illustrate the proposed methods.

Suggested Citation

  • Conghua Cheng & Jinyuan Chen & Jianming Bai, 2013. "Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1464-1479, July.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:7:p:1464-1479
    DOI: 10.1080/02664763.2013.788613
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2013.788613
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2013.788613?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. 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.
    2. 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.
    3. Zeinab H. Amin, 2007. "Tests for the Validity of the Assumption that the Underlying Distribution of Life is Pareto," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(2), pages 195-201.
    4. Siu-Keung Tse & Chunyan Yang, 2003. "Reliability sampling plans for the Weibull distribution under Type II progressive censoring with binomial removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 709-718.
    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. Ali Akbar Jafari & Javad Shaabani, 2020. "Comparing scale parameters in several gamma distributions with known shapes," Computational Statistics, Springer, vol. 35(4), pages 1927-1950, December.
    2. Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
    3. Malekzadeh, Ahad & Kharrati-Kopaei, Mahmood, 2017. "An exact method for making inferences on the common location parameter of several heterogeneous exponential populations: Complete and censored data," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 210-215.

    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. Mohamed Sief & Xinsheng Liu & Abd El-Raheem Mohamed Abd El-Raheem, 2024. "Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution," Computational Statistics, Springer, vol. 39(5), pages 2791-2820, July.
    2. Maram Salem & Zeinab Amin & Moshira Ismail, 2020. "Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 1-33, May.
    3. Amit Singh Nayal & Bhupendra Singh & Vrijesh Tripathi & Abhishek Tyagi, 2024. "Analyzing stress-strength reliability $$\delta =\text{ P }[U," 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. 15(6), pages 2453-2472, June.
    4. 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.
    5. 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.
    6. 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.
    7. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    8. 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.
    9. 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.
    10. Amal S. Hassan & Rana M. Mousa & Mahmoud H. Abu-Moussa, 2024. "Bayesian Analysis of Generalized Inverted Exponential Distribution Based on Generalized Progressive Hybrid Censoring Competing Risks Data," Annals of Data Science, Springer, vol. 11(4), pages 1225-1264, August.
    11. 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.
    12. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    13. Wenjie Zhang & Wenhao Gui, 2022. "Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    14. Devendra Kumar & M. Nassar & Sanku Dey, 2023. "Progressive Type-II Censored Data and Associated Inference with Application Based on Li–Li Rayleigh Distribution," Annals of Data Science, Springer, vol. 10(1), pages 43-71, February.
    15. 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.
    16. 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.
    17. Hanan Haj Ahmad & Mohamed Aboshady & Mahmoud Mansour, 2024. "The Role of Risk Factors in System Performance: A Comprehensive Study with Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 12(11), pages 1-21, June.
    18. Fu, Jiayu & Xu, Ancha & Tang, Yincai, 2012. "Objective Bayesian analysis of Pareto distribution under progressive Type-II censoring," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1829-1836.
    19. Mansour Shrahili & Naif Alotaibi & Devendra Kumar & Salem A. Alyami, 2020. "Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    20. Sen, Ananda & Kannan, Nandini & Kundu, Debasis, 2013. "Bayesian planning and inference of a progressively censored sample from linear hazard rate distribution," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 108-121.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:40:y:2013:i:7:p:1464-1479. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.