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Empirical Bayes estimator of parameter, reliability and hazard rate for Kumaraswamy distribution

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Abstract

This paper proposes empirical Bayes estimators of parameter, reliability and hazard function for Kumaraswamy distribution under the linear exponential loss function for progressively type II censored samples with binomial removal and type II censored samples. The proposed estimators have been compared with the corresponding Bayes estimators for their simulated risks. The applicability of the proposed estimators have been illustrated through ulcer patient data.

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References

  • Aarset MV (1987) How to identify bathtub hazard rate. IEEE Trans Reliabil 36(1):106–108

    Article  Google Scholar 

  • Amin EA (2017) Estimation of stress-strength reliability for Kumaraswamy exponential distribution based on upper record values. Int J Contemp Math Sci 2(2):59–71

    Article  MathSciNet  Google Scholar 

  • Balakrishnan N, Aggarwalla R (2000) Progressive censoring: theory, methods and applications. Birkhauser, Boston

    Book  Google Scholar 

  • Balakrishnan N, Sandhu RA (1995) A simple simulation algorithm for generating progressive type II censored samples. Am Stat 49(2):229–230

    Google Scholar 

  • Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, New York

    Book  Google Scholar 

  • Cohen AC (1963) Progressively censored samples in life testing. Technometries 5(3):327–339

    Article  MathSciNet  Google Scholar 

  • Collett D (2003) Modelling survival data in medical research. Chapman and Hall, Boca Raton

    MATH  Google Scholar 

  • Gholizadeh R, Khlilpor M, Hsadian M (2011) Bayesian estimation in the Kumaraswamy distribution under progressively type II censoring data. Int J Eng Sci Technol 3(9):47–65

    Google Scholar 

  • Ihaka R, Gentleman R (1996) R: a language for data analysis and graphics. J Comput Graph Stat 5(3):299–314

    Google Scholar 

  • Jones MC (2009) Kumaraswamy’s distribution: a beta-type distribution with some tractability advantages. Stat Methodol 6(1):70–81

    Article  MathSciNet  Google Scholar 

  • Kim C, Jung J, Chung Y (2011) Bayesian estimation for the exponentiated Weibull model under type II progressive censoring. Stat Pap 52(1):53–70

    Article  MathSciNet  Google Scholar 

  • Kohansal A (2017) On estimation of reliability in a multicomponent stress-strength model for Kumaraswamy exponential distribution based on progressively censored sample. Stat Pap 2017:1–40

    Google Scholar 

  • Kumaraswamy P (1980) A generalized probability density function for double-bounded random processes. J Hydrol 46(1–2):79–88

    Article  Google Scholar 

  • Lemonte AJ (2011) Improved point estimation for the Kumaraswamy distribution. J Stat Comput Simul 81(12):1971–1982

    Article  MathSciNet  Google Scholar 

  • Mitnik PA (2013) New properties of the Kumaraswamy distribution. Commun Stat Theory Methods 42(5):741–755

    Article  MathSciNet  Google Scholar 

  • Morris CN (1983) Parametric empirical Bayes inference: theory and applications. J Am Stat Assoc 78(381):47–55

    Article  MathSciNet  Google Scholar 

  • Nassar MM, Eissa FH (2005) Bayesian estimation for the exponentiated Weibull model. Commun Stat Theory Methods 33(10):2343–2362

    Article  MathSciNet  Google Scholar 

  • Shi Y, Shi X, Xu Y (2005) Approximate confidence limits of reliability performances for cold standby series system. J Appl Math Comput 19(1–2):439–445

    Article  MathSciNet  Google Scholar 

  • Tse SK, Yang C, Yuen HK (2000) Statistical analysis of Weibull distributed life time data under type II progressive censoring with binomial removals. J Appl Stat 27(8):1033–1043

    Article  Google Scholar 

  • Varian HR (1975) A Bayesian approach to real estate assessment. Studies in Bayesian econometric and statistics in honor of Leonard J. Savage 1975:195–208

    Google Scholar 

  • Yan S, Gendai G (2003) Bayes estimation for reliability indexes of cold standby system. J N China Electr Power Univ 30(2):96–99

    Google Scholar 

  • Zellner A (1986) A Bayesian estimation and prediction using asymmetric loss function. J Am Sat Assoc 81(394):446–451

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the comments and suggestions by the referees and the editors. Their comments and suggestions have greatly improved the paper.

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Authors and Affiliations

  1. Department of Statistics, Central University of Haryana, Mahendergarh, 123031, India

    Manoj Kumar & Anurag Pathak

  2. Department of Statistics, Banaras Hindu University, Varanasi, 221005, India

    Sanjay Kumar Singh & Umesh Singh

Authors
  1. Manoj Kumar
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  2. Sanjay Kumar Singh
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  3. Umesh Singh
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  4. Anurag Pathak
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Correspondence to Manoj Kumar.

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Kumar, M., Singh, S.K., Singh, U. et al. Empirical Bayes estimator of parameter, reliability and hazard rate for Kumaraswamy distribution. Life Cycle Reliab Saf Eng 8, 243–256 (2019). https://doi.org/10.1007/s41872-019-00085-0

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  • DOI: https://doi.org/10.1007/s41872-019-00085-0

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