Maximum likelihood estimation based on type-i hybrid progressive censored competing risks data

  • Authors

    • Samir Ashour Department of Mathematical Statistics Institute of Statistical Studies and Research Cairo University
    • Wael Abu El Azm Department of Statistics Faculty of Commerce Zagazig University
    2016-03-13
    https://doi.org/10.14419/ijasp.v4i1.5735
  • Competing Risks, Type-I Progressive Hybrid Censoring, Generalized Weibull Distributions, Generalized Exponential Distribution, Weibull Distributions, Exponential Distribution, Maximum Likelihood Estimation, Asymptotic Confidence Interval.

  • Abstract

    This paper is concerned with the estimators problems of the generalized Weibull distribution based on Type-I hybrid progressive censoring scheme (Type-I PHCS) in the presence of competing risks when the cause of failure of each item is known. Maximum likelihood estimates and the corresponding Fisher information matrix are obtained. We generalized Kundu and Joarder [7] results in the case of the exponential distribution while, the corresponding results in the case of the generalized exponential and Weibull distributions may be obtained as a special cases. A real data set is used to illustrate the theoretical results.

  • References

    1. [1] Akaike, H. (1969). Fitting autoregressive models for regression. Annals of Institute of Statistical Mathematics, 21, 243–7. http://dx.doi.org/10.1007/BF02532251.

      [2] Childs, A., Chandrasekar, B. and Balakrishnan, N. (2008). Exact likelihood inference for an exponential parameter under progressive hybrid censoring. In: Vonta, F., Nikulin, M., Limnios, N., Huber-Carol, C. (Eds.), Statistical Models and Methods for Biomedical and Technical Systems. Birkhuser, Boston, MA, 319–330. http://dx.doi.org/10.1007/978-0-8176-4619-6_23.

      [3] Cohen, A. C. (1965). Maximum likelihood estimation in the Weibull distribution based on complete and censored samples. Technometrics, 5, 579-588. http://dx.doi.org/10.1080/00401706.1965.10490300.

      [4] Epstein, B. (1954). Truncated life-test in exponential case. Annals of Mathematical Statistics, 25, 555–564. http://dx.doi.org/10.1214/aoms/1177728723.

      [5] Hashemi, R. and Azar. J. (2011). Analysis of competing risks in the Burr XII model in presence of progressive hybrid censoring. International Mathematical Forum, 6, 3069 – 3078.

      [6] Hoel, D. G. (1972). A representation of mortality data by competing risks. Biometrics, 28, 475-488. http://dx.doi.org/10.2307/2556161.

      [7] Kundu, D. and Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics and Data Analysis, 50, 2509–2528. http://dx.doi.org/10.1016/j.csda.2005.05.002.

      [8] Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. http://dx.doi.org/10.1214/aos/1176344136.

      [9] Sarhan, A.M. (2007). Analysis of incomplete, censored data in competing risks models with generalized exponential distributions. IEEE Transactions on Reliability, 58, 132-138. http://dx.doi.org/10.1109/TR.2006.890899.

      [10] Sarhan, A.M., Al-Amri, M. and Alwasel, I. (2013). Analysis of a competing risks models with generalized Weibull distribution. Pakistan Journal of Statistics, 29, 271-281.

  • Downloads

  • Received date: 2016-01-07

    Accepted date: 2016-01-28

    Published date: 2016-03-13