OJS  Vol.4 No.8 , September 2014
Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution
Abstract: This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.
Cite this paper: Ahmed, A. (2014) Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution. Open Journal of Statistics, 4, 570-577. doi: 10.4236/ojs.2014.48053.

[1]   Cohen, C.A. and Whitten, B. (1982) Modified Maximum Likelihood and Modified Moment Estimators for the Three-Parameter Weibull Distribution. Communications in Statistics-Theory and Methods, 11, 2631-2656.

[2]   Sinha, S.K. (1986) Bayes Estimation of the Reliability Function and Hazard Rate of a Weibull Failure Time Distribution. Trabajos de Estadística, 1, 47-56.

[3]   Smith, R.L. and Naylor, J. (1987) A Comparison of Maximum Likelihood and Bayesian Estimators for the Three-Parameter Weibull Distribution. Applied Statistics, 36, 358-369.

[4]   Singh, U., Gupta, P.K. and Upadhyay, S. (2002) Estimation of Exponentiated Weibull Shape Parameters under LINEX Loss Function. Communications in Statistics-Simulation and Computation, 31, 523-537.

[5]   Hossain, A.M. and Zimmer, W.J. (2003) Comparison of Estimation Methods for Weibull Parameters: Complete and Censored Samples. Journal of Statistical Computation and Simulation, 73, 145-153.

[6]   Nassar, M. and Eissa, F.H. (2005) Bayesian Estimation for the Exponentiated Weibull Model. Communications in Statistics—Theory and Methods, 33, 2343-2362.

[7]   Soliman, A.A., Abd Ellah, A.H. and Sultan, K.S. (2006) Comparison of Estimates Using Record Statistics from Weibull Model: Bayesian and Non-Bayesian Approaches. Computational Statistics & Data Analysis, 51, 2065-2077.

[8]   Kantar, Y.M. and Senoglu, B. (2008) A Comparative Study for the Location and Scale Parameters of the Weibull Distribution with Given Shape Parameter. Computers Geosciences, 34, 1900-1909.

[9]   Gupta, A., Mukherjee, B. and Upadhyay, S. (2008) Weibull Extension Model: A Bayes Study Using Markov Chain Monte Carlo Simulation. Reliability Engineering & System Safety, 93, 1434-1443.

[10]   Kundu, D. and Howlader, H. (2010) Bayesian Inference and Prediction of the Inverse Weibull Distribution for Type-II Censored Data. Computational Statistics & Data Analysis, 54, 1547-1558.

[11]   Pandey, B., Dwividi, N. and Pulastya, B. (2011) 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, 55, 163-172.

[12]   Flygare, M.E. and Buckwalter, J.A. (1985) Maximum Likelihood Estimation for the 2-Parameter Weibull Distribution Based on Interval-Data. IEEE Transactions on Reliability, 34, 57-60.

[13]   Al Omari, M.A., Ibrahim, N.A., Arasan, J. and Adam, M.B. (2012) Extension of Jeffreys’s Prior Estimate for Weibull Censored Data Using Lindley’s Approximation. Australian Journal of Basic and Applied Sciences, 5, 884-889.

[14]   Hastings, W.K. (1970) Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika, 57, 97-109.

[15]   Soliman, A.A., Abd-Ellah, A.H., Abou-Elheggag, N.A. and Ahmed, E.A. (2011) Modified Weibull Model: A Bayes Study Using MCMC Approach Based on Progressive Censoring Data. Reliability Engineering & System Safety, 100, 48-57.

[16]   Al Omari, M.A., Ibrahim, N.A., Arasan, J. and Adam, M.B. (2012) Bayesian Survival and Hazard Estimate for Weibull Censored Time Distribution. Journal of Applied Sciences, 12, 1313-1317.