Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution

  • M. S. Panwar
  • Sanjeev K Tomer Department of Statistics, Banaras Hindu University.


In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell distribution assuming an $\varepsilon$-contamination class of prior distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.


Balakrishnan, N. and Aggarwala, R. (2000). Progressive Censoring: Theory, Methods and Applications. Birkhauser, Boston.

Balakrishnan, N. and Kundu, D. (2012). Hybrid censoring: Models, inferential results and applications. Computational Statistics & Data Analysis, 57:166–209.

Berger, J. (1982). Bayesian robustness and the stein effect. Journal of the American Statistical Association, 77(378):358–368.

Berger, J. (1984). The robust Bayesian viewpoint (with discussion): Robustness in Bayesian statistics.

Berger, J. and Berliner, L. M. (1986). Robust Bayes and empirical Bayes analysis with ε-contaminated priors. The Annals of Statistics, pages 461–486.

Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer - Verlag., New York.

Chaturvedi, A. (1996). Robust Bayesian analysis of the linear regression model.Journal of statistical planning and inference, 50(2):175–186.

Chaturvedi, A., Pati, M., and Tomer, S. K. (2014). Robust Bayesian analysis of Weibull failure model. Metron, 72(1):77–95.

Childs, A., Chandrasekar, B., and Balakrishnan, N. (2007). Exact likelihood inference for an exponential parameter under progressive hybrid censoring.

Statistical Models and Methods for Biomedical and Technical Systems(Eds., F. Vonta, M. Nikulin, N. Limnios and C. Huber-Carol), pages 323 – 334.

Good, I. J. (1965). The estimation of probabilities: An essay on modern Bayesian methods, volume 258. MIT press Cambridge, MA.

Good, I. J. (1983). Good thinking: The foundations of probability and its appli-cations. U of Minnesota Press.

Krishna, H. and Malik, M. (2009). Relaibility estimation of Maxwell distribution with type-II censored data. International Journal of Quality & Reliability Management, 26(2):184–195.

Krishna, H. and Malik, M. (2012). Reliability estimation in Maxwell distribution with progressively type-II censored data. Journal of Statistical Computation and Simulation, 82(4):623–641.

Kundu, D. and Jordar, A. (2006). Analysis of type-II progressively hybrid censored data. Computational Statistics & Data Analysis, 50:2509 – 2528.

Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. John Wiley and Sons Inc, New York, 2nd edition.

Sinha, S. K. (1986). Reliability and Life Testing. John Wiley & Sons, Inc.

Tomer, S. K. and Panwar, M. S. (2015). Estimation procedures for Maxwell distribution under Type-I progressively hybrid censoring scheme. Journal of Statistical Computation and Simulation, 85:339–356.

How to Cite
Panwar, M. S., & Tomer, S. K. (2018). Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution. Austrian Journal of Statistics, 48(1), 38-55.
Special Issue on Lifetime Data Modelling (closed)