IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i4d10.1007_s00362-016-0866-4.html
   My bibliography  Save this article

From B-spline representations to gamma representations in hybrid censoring

Author

Listed:
  • Julian Górny

    (RWTH Aachen University)

  • Erhard Cramer

    (RWTH Aachen University)

Abstract

We establish an identity that relates B-spline functions to linear combinations of gamma density functions. Utilizing this connection, we illustrate that, for exponentially distributed lifetimes, the distribution of the MLE in various hybrid censoring schemes can be expressed in terms of gamma density functions with simple weights. As an example, representations for the density functions in the case of Type-I sequential, Type-II progressive hybrid, generalized Type-I progressive hybrid, and generalized Type-II progressive hybrid censoring schemes are presented. It turns out that the representations arising from the spacings’ based approach introduced in Cramer and Balakrishnan (Stat Methodol 10:128–150, 2013) are more compact than those available in the literature so far.

Suggested Citation

  • Julian Górny & Erhard Cramer, 2019. "From B-spline representations to gamma representations in hybrid censoring," Statistical Papers, Springer, vol. 60(4), pages 1119-1135, August.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0866-4
    DOI: 10.1007/s00362-016-0866-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0866-4
    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/s00362-016-0866-4?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. Ping Chan & Hon Ng & Feng Su, 2015. "Exact likelihood inference for the two-parameter exponential distribution under Type-II progressively hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 747-770, August.
    2. N. Balakrishnan & Qihao Xie & D. Kundu, 2009. "Exact inference for a simple step-stress model from the exponential distribution under time constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 251-274, March.
    3. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    4. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    5. Maria Kateri & Udo Kamps, 2015. "Inference in step-stress models based on failure rates," Statistical Papers, Springer, vol. 56(3), pages 639-660, August.
    6. S. Gurler, 2012. "On residual lifetimes in sequential (n − k + 1)-out-of-n systems," Statistical Papers, Springer, vol. 53(1), pages 23-31, February.
    7. Soltani, Ahmad Reza & Roozegar, Rasool, 2012. "On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1012-1020.
    Full references (including those not matched with items on IDEAS)

    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. Arnab Koley & Debasis Kundu, 2017. "On generalized progressive hybrid censoring in presence of competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 401-426, May.
    2. Julian Górny & Erhard Cramer, 2020. "On Exact Inferential Results for a Simple Step-Stress Model Under a Time Constraint," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 201-239, November.
    3. 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.
    4. Tzong-Ru Tsai & Yuhlong Lio & Wei-Chen Ting, 2021. "EM Algorithm for Mixture Distributions Model with Type-I Hybrid Censoring Scheme," Mathematics, MDPI, vol. 9(19), pages 1-18, October.
    5. Suparna Basu & Sanjay K. Singh & Umesh Singh, 2019. "Estimation of Inverse Lindley Distribution Using Product of Spacings Function for Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1377-1394, December.
    6. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    7. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    8. Julian Górny & Erhard Cramer, 2018. "Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 173-210, February.
    9. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.
    10. Mukhtar M Salah & Essam A Ahmed & Ziyad A Alhussain & Hanan Haj Ahmed & M El-Morshedy & M S Eliwa, 2021. "Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-16, January.
    11. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    12. Ping Chan & Hon Ng & Feng Su, 2015. "Exact likelihood inference for the two-parameter exponential distribution under Type-II progressively hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 747-770, August.
    13. Tanmay Sen & Yogesh Mani Tripathi & Ritwik Bhattacharya, 2018. "Statistical Inference and Optimum Life Testing Plans Under Type-II Hybrid Censoring Scheme," Annals of Data Science, Springer, vol. 5(4), pages 679-708, December.
    14. Subhankar Dutta & Suchandan Kayal, 2023. "Inference of a competing risks model with partially observed failure causes under improved adaptive type-II progressive censoring," Journal of Risk and Reliability, , vol. 237(4), pages 765-780, August.
    15. N. Balakrishnan & G. Iliopoulos, 2010. "Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 89-109, July.
    16. Abhimanyu Singh Yadav & Emrah Altun & Haitham M. Yousof, 2021. "Burr–Hatke Exponential Distribution: A Decreasing Failure Rate Model, Statistical Inference and Applications," Annals of Data Science, Springer, vol. 8(2), pages 241-260, June.
    17. Rui Hua & Wenhao Gui, 2022. "Inference for copula-based dependent competing risks model with step-stress accelerated life test under generalized progressive hybrid censoring," Computational Statistics, Springer, vol. 37(5), pages 2399-2436, November.
    18. O. E. Abo-Kasem & Ehab M. Almetwally & Wael S. Abu El Azm, 2023. "Inferential Survival Analysis for Inverted NH Distribution Under Adaptive Progressive Hybrid Censoring with Application of Transformer Insulation," Annals of Data Science, Springer, vol. 10(5), pages 1237-1284, October.
    19. Hassan Okasha & Yuhlong Lio & Mohammed Albassam, 2021. "On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme," Mathematics, MDPI, vol. 9(22), pages 1-38, November.
    20. Ritwik Bhattacharya & Baidya Nath Saha & Graceila González Farías & Narayanaswamy Balakrishnan, 2020. "Multi-criteria-based optimal life-testing plans under hybrid censoring scheme," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 430-453, June.

    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:60:y:2019:i:4:d:10.1007_s00362-016-0866-4. 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.