Bayesian inference for Rayleigh distribution under hybrid censoring

  • A. Asgharzadeh
  • M. Azizpour
Original Article


In this paper, and based on a hybrid censored sample from a Rayleigh distribution, Bayes estimators and highest posterior density credible intervals are obtained for the unknown parameter, and some lifetime parameters such as the reliability and hazard rate functions. Bayes estimators are obtained using squared error and linear–exponential loss functions. We also obtain the Bayes predictive estimator and %95 prediction interval for future observations. Finally, a numerical example is given to illustrate the application of the results and Monte Carlo simulations are performed to compare the performances of the different methods.


Bayesian estimation Hybrid censoring Bayesian prediction Rayleigh distribution 

Mathematics Subject Classification

62N01 62M20 62F15 


  1. Ahmadi J, Doostparast M, Parsian A (2005) Estimation and prediction in a two parameter exponential distribution based on k-record values under LINEX loss function. Commun Stat Theory Methods 34:795–805MathSciNetCrossRefzbMATHGoogle Scholar
  2. Asgharzadeh A, Fallah A (2011) Estimation and prediction for exponentiated family of distributions based on records. Commun Stat Theory Methods 40:68–83MathSciNetCrossRefzbMATHGoogle Scholar
  3. Balakrishnan N, Kundu D (2013) Hybrid censoring: models, inferential results and applications. Comput Stat Data Anal 57:166–209MathSciNetCrossRefGoogle Scholar
  4. Basu AP, Ebrahimi N (1991) Bayesian approach to life testing and reliability estimation using asymmetric loss function. J Stat Plan Inference 29:21–31MathSciNetCrossRefzbMATHGoogle Scholar
  5. Bernardo JM, Smith AFM (1994) Bayesian theory. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  6. Chen S, Bhattachacharya GK (1988) Exact confidence bounds for an exponential parameter under hybrid censoring. Commun Stat Theory Methods 17:1857–1870MathSciNetCrossRefzbMATHGoogle Scholar
  7. Childs A, Chandrasekhar B, Balakrishnan N, Kundu D (2003) Exact likelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 55:319–330MathSciNetzbMATHGoogle Scholar
  8. Draper N, Guttman I (1987) Bayesian analysis of hybrid life tests with exponential failure times. Ann Inst Stat Math 39:219–225MathSciNetCrossRefzbMATHGoogle Scholar
  9. Ebrahimi N (1986) Estimating the parameter of an exponential distribution from hybrid life test. J Stat Plan Inference 14:255–261MathSciNetCrossRefzbMATHGoogle Scholar
  10. Epstein B (1954) Truncated life tests in the exponentioal case. Ann Stat 25:555–564CrossRefzbMATHGoogle Scholar
  11. Fernandez AJ (2000) Bayesian inference from type II doubly censored Rayleigh data. Stat Probab Lett 48:393–399MathSciNetCrossRefzbMATHGoogle Scholar
  12. Feynman RP (1987) Mr. Feynman goes to Washington. Engineering and Science. California Institute of Technology, PasadenaGoogle Scholar
  13. Gupta DR, Kundu D (1998) Hybrid censoring schemes with exponential failure distribution. Commun Stat Theory Methods 27:3065–3083CrossRefzbMATHGoogle Scholar
  14. Howlader HA, Hossain A (1995) On Bayesian estimation and prediction from Rayleigh based on type II censored data. Commun Stat Theory Methods 24:2249–2259MathSciNetCrossRefzbMATHGoogle Scholar
  15. Jeong HS, Park JI, Yum BJ (1996) Development of \((r, T)\) hybrid sampling plans for exponential lifetime distributions. J Appl Stat 23:601–607CrossRefGoogle Scholar
  16. Kundu D, Joarder A (2006) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528MathSciNetCrossRefzbMATHGoogle Scholar
  17. Kundu D, Pradhan B (2009) Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring. Commun Stat Theory Methods 38:2030–2041MathSciNetCrossRefzbMATHGoogle Scholar
  18. Lawless JF (1982) Stat models methods for lifetime data. Wiley, New YorkzbMATHGoogle Scholar
  19. Lin CT, Ng HKT, Chan PS (2009) Statistical inference of Type-II progressively hybrid censored data with Weibull lifetimes. Commun Stat Theory Methods 38:1710–1729MathSciNetCrossRefzbMATHGoogle Scholar
  20. Ng HKT, Kundu D, Chan PS (2009) Statistical analysis of exponential lifetimes under an adaptive hybrid Type-II progressive censoring scheme. Nav Res Logist 56:687–698MathSciNetCrossRefzbMATHGoogle Scholar
  21. Polovko AM (1986) Fundamentals of reliability theory. Academic Press, New YorkzbMATHGoogle Scholar
  22. Raqab MZ, Madi MT (2002) Bayesian prediction of the total time on test using doubly censored Rayleigh data. J Stat Comput Simul 72:781–789MathSciNetCrossRefzbMATHGoogle Scholar
  23. Ren C, Sun D, Dey DK (2006) Bayesian and frequentist estimations and prediction for exponential distributions. J Stat Plan Inference 13:2873–2897MathSciNetCrossRefzbMATHGoogle Scholar
  24. Soliman AA, Al-Aboud FM (2008) Baysian inference using record values from Rayleigh model with application. Eur J Oper Res 185:252–272CrossRefzbMATHGoogle Scholar
  25. Wu S, Chen D, Chen S (2006) Baysian inference for Rayleigh distribution under progressive censored sample. Appl Stoch Models Bus Ind 26:126–279Google Scholar
  26. Varian HR (1975) A Bayesian approach to real estate assessment. In: Finberg SE, Zellner A (eds) Studies in Bayesian econometrics and statistics in honor of Leonard J. Sarage. North Holland, Amsterdam, pp 195–208Google Scholar
  27. Zellner A (1986) Bayesian estimation and prediction using asymmetric loss function. J Am Stat Assoc 81:446–451MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2014

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of MazandaranBabolsarIran

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