Bayesian estimation of two-parameter Weibull distribution using extension of Jeffreys prior information with three loss functions. (English) Zbl 1264.62023

Summary: The Weibull distribution has been observed as one of the most useful distribution for modelling and analysing life time data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method for estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameter estimation which is in contention with other estimation methods. We examine the performance of the maximum likelihood estimator and Bayesian estimator using extensions of the Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using the mean squared error through simulation studies with varying sample sizes. The results show that the Bayesian estimator using extensions of Jeffreys’ prior under linear exponential loss functions in most cases gives the smallest mean squared error and the absolute bias for both the scale parameter \(\alpha\) and the shape parameter \(\beta\) for the given values of the extension of Jeffreys’ prior.


62F15 Bayesian inference
62F10 Point estimation
Full Text: DOI


[1] L. F. Zhang, M. Xie, and L. C. Tang, “On weighted least square estimation for the parameters of Weibull distribution,” in Recent Advances in Reliability and Quality Design, P. Hoang, Ed., pp. 57-84, Springer, London, UK, 2008. · Zbl 1266.62087
[2] R. B. Abernethy, The New Weibull Handbook, 5th edition, 2006. · Zbl 0876.62081
[3] M. A. Al Omari and N. A. Ibrahim, “Bayesian survival estimation for Weibull distribution with censored data,” Journal of Applied Sciences, vol. 11, no. 2, pp. 393-396, 2011.
[4] F. M. Al-Aboud, “Bayesian estimations for the extreme value distribution using progressive censored data and asymmetric loss,” International Mathematical Forum, vol. 4, no. 33, pp. 1603-1622, 2009. · Zbl 1279.62063
[5] H. S. Al-Kutubi and N. A. Ibrahim, “Bayes estimator for exponential distribution with extension of Jeffery prior information,” Malaysian Journal of Mathematical Sciences, vol. 3, no. 2, pp. 297-313, 2009.
[6] B. N. Pandey, N. Dwividi, and B. Pulastya, “Comparison between bayesian and maximum likelihood estimation of the scale parameter in Weibull distribution with known shape under linex loss function,” Journal of Scientific Research, vol. 55, pp. 163-172, 2011.
[7] F. M. Al-Athari, “Parameter estimation for the double-pareto distribution,” Journal of Mathematics and Statistics, vol. 7, no. 4, pp. 289-294, 2011. · Zbl 1306.62067
[8] A. Hossain and W. Zimmer, “Comparison of estimation methods for Weibull parameters: complete and censored samples,” Journal of Statistical Computation and Simulation, vol. 73, no. 2, pp. 145-153, 2003. · Zbl 1014.62018 · doi:10.1080/0094965021000033486
[9] L. M. Lye, K. P. Hapuarachchi, and S. Ryan, “Bayes estimation of the extreme-value reliability,” IEEE Transactions on Reliability, vol. 42, no. 4, pp. 641-644, 1993. · Zbl 0797.62093 · doi:10.1109/24.273598
[10] A. Zellner, “Bayesian estimation and prediction using asymmetric loss functions,” Journal of the American Statistical Association, vol. 81, no. 394, pp. 446-451, 1986. · Zbl 0603.62037 · doi:10.2307/2289234
[11] S. K. Sinha, “Byaes estimation of the reliability function and hazard rate of a Weibull failure time distribution,” Tranbajos De Estadistica, vol. 1, no. 2, pp. 47-56, 1986.
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