Bayesian Inference for the Parameters of Two-Parameter Exponential Lifetime Models Based on Type-I and Type-II Censoring

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 229)

Abstract

The parameters of the two-parameter exponential distribution are estimated in this chapter from the Bayesian viewpoint based on complete, Type-I and Type-II censored samples. Bayes point estimates and credible intervals of the unknown parameters are proposed under the assumption of suitable priors on the unknown parameters and under the assumption of the squared error loss function. Illustrative example is provided to motivate the proposed Bayes point estimates and the credible intervals. Various Monte Carlo simulations are also performed to compare the performances of the classical and Bayes estimates.

Keywords

Bayes estimate Censored samples Credible interval Maximum likelihood estimate Mean squared error  Squared error loss function 

References

  1. 1.
    Balakrishnan N, Basu AP (1995) The exponential distribution: theory, methods and applications. Gordon and Breach Publishers, Newark, NJGoogle Scholar
  2. 2.
    El-Sayyed GM (1967) Estimation of the parameter of an exponential distribution. J Roy Stat Soc: Ser B (Stat Methodol) 29:525–532Google Scholar
  3. 3.
    Singh RS, Prasad B (1989) Uniformly strongly consistent prior distribution and empirical Bayes estimators with asymptotic optimality and rates in a non-exponential family. Sankhya A51:334–342MathSciNetGoogle Scholar
  4. 4.
    Prasad B, Singh RS (1990) Estimation of prior distribution and empirical Bayes estimation in a non-exponential family. J Stat Plan Infer 24:81–86MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Sarhan AM (2003) Empirical Bayes estimates in exponential reliability model. Appl Math Comput 135:319–332MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Singh U, Kumar A (2005) Shrinkage estimators for exponential scale parameter under multiply Type II censoring. Aust J Stat 34:39–49Google Scholar
  7. 7.
    Singh U, Kumar A (2005) Bayes estimator for one parameter exponential distribution under multiply-II censoring. Indian J Math Math Sci 1:23–33Google Scholar
  8. 8.
    Singh U, Kumar A (2007) Bayesian estimation of the exponential parameter under a multiply Type-II censoring scheme. Austrian J Stat 36(3):227–238Google Scholar
  9. 9.
    Shi Y, Yan W (2010) The EB estimation of scale-parameter for two-parameter exponential distribution under the Type-I censoring life test. J Phys Sci 14:25–30Google Scholar
  10. 10.
    Bayoud HA (2012) Bayesian analysis of Type-I censored sample from two-parameter exponential distribution. In: Lecture notes in engineering and computer science: proceedings of the world congress on engineering, WCE (2012), 4–6 July 2012 U.K , London, pp 291–296Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Fahad Bin Sultan UniversityTabukSaudi Arabia

Personalised recommendations