Skip to main content
SpringerLink
Log in

Exact inference for joint Type-I hybrid censoring model with exponential competing risks data

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates (MLEs) of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function (MGF). Confidence intervals (CIs) of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balakrishnan, N., Han, D. Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring. Journal of Statistical Planning and Inference, 138: 4172–4186 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Balakrishnan, N., Kundu, D. Hybrid censoring: Models, inferential results and applications. Computational Statistics & Data Analysis, 57: 166–209 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Balakrishnan, N., Rasouli, A. Exact likelihood inference for two exponential populations under joint Type-II censoring. Computational Statistics & Data Analysis, 52: 2725–2738 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bhattacharyya, G.K. Inferences under two-sample and multi-sample situations. In: The Exponential Distribution: Theory, Methods and Applications, ed. By Balakrishnan N. and Basu A.P., Newark: Gordon and Breach, 1995, 93–118

    Google Scholar 

  5. Bunea, C., Mazzuchi, T. Competing failure modes in accelerated life testing. Journal of statistical planning and inference, 136: 1608–1620 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Childs, A., Chandrasekar, B., Balakrishnan, N., Kundu, D. Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Annals of the Institute of Statistical Mathematics, 55: 319–330 (2003)

    MathSciNet  MATH  Google Scholar 

  7. Cox, D.R. The analysis of exponentially distributed life-times with two types of failure. Journal of the Royal Statistical Society. Series B (Methodological), 21: 411–421 (1959)

    MathSciNet  MATH  Google Scholar 

  8. Epstein, B. Truncated life tests in the exponential case. The Annals of Mathematical Statistics, 555–564 (1954)

    Google Scholar 

  9. Doostparast, M., Ahmadi, M.V., Ahmadi, J. Bayes estimation based on joint progressive Type-II censored data under Linex loss function. Communications in Statistics-Simulation and Computation, 42: 1865–1886 (2013)

    MathSciNet  MATH  Google Scholar 

  10. Han, D., Balakrishnan, N. Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint. Computational Statistics & Data Analysis, 54: 2066–2081 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, G, Lin, C. Analysis of two-sample censored data using a semiparametric mixture model. Acta Mathematicae Applicatae Sinica (English Series), 25: 389–398 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lin, C.T., Ke, S.J. Estimation of P(Y < X) for Location-Scale distributions under Joint Progressively Type-II right censoring. Quality Technology and Quantitative Management, 10: 339–352 (2013)

    Article  Google Scholar 

  13. Park, S., Balakrishnan, N., Zheng, G. Fisher information in hybrid censored data. Statistics & Probability Letters, 78: 2781–2786 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Parsi, S., Ganjali, M., Farsipour, N.S. Conditional Maximum Likelihood and Interval Estimation for Two Weibull Populations under Joint Type-II Progressive Censoring. Communications in Statistics-theory and Methods, 40: 2117–2135 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Peng, X, Yan, Z. Bayesian estimation for generalized exponential distribution based on progressive type-I interval censoring. Acta Mathematicae Applicatae Sinica (English Series), 29: 391–402 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rasouli, A., Balakrishnan, N. Exact likelihood inference for two exponential populations under joint progressive type-II censoring. Communications in Statistics-Theory and Methods, 39: 2172–2191 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sarhan, A.M., Alameri, M., Al-Wasel I. Analysis of Progressive Censoring Competing Risks Data with Binomial Removals. International Journal of Mathmatics Analysis, 2: 965–976 (2008)

    MathSciNet  MATH  Google Scholar 

  18. Zhang, F, Zhou, Y. Analyzing left-truncated and right-censored data under Cox models with long-term survivors. Acta Mathematicae Applicatae Sinica (English Series), 29: 241–252 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhou, Y., Wu, G.F. Sequential fixed-width confidence intervals of quantiles for truncated and censored data. Acta Mathematicae Applicatae Sinica, 25: 204–215 (2002)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics and Management, Shanxi University, Taiyuan, 030006, China

    Song Mao

  2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Yi-min Shi

  3. 78020 Unit, Kunming, 655000, China

    Xiao-lin Wang

Authors
  1. Song Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi-min Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiao-lin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Song Mao.

Additional information

Supported by the National Natural Science Foundation of China (No.71571144), Natural Science Basic Research Program of Shaanxi Province (2015JM1003), the Program of International Cooperation and Exchanges in Science and Technology Funded by Shanxi Province(2016KW-033), Shanxi Scholarship Council of China (2016-015).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, S., Shi, Ym. & Wang, Xl. Exact inference for joint Type-I hybrid censoring model with exponential competing risks data. Acta Math. Appl. Sin. Engl. Ser. 33, 645–658 (2017). https://doi.org/10.1007/s10255-017-0688-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-017-0688-8

Keywords

2000 MR Subject Classification

Search

Navigation