COMPARISON OF PARAMETER ESTIMATION METHODS IN WEIBULL DISTRIBUTION

Year 2020, Volume: 38 Issue: 3, 1609 - 1621, 05.10.2021

Esin Köksal Babacan Samet Kaya

Abstract

The main objective of this study is to compare the parameter estimation methods for Weibull distribution. We consider maximum likelihood and Bayes estimation methods for the scale and shape parameters of Weibull distribution. While computing the Bayes estimates for a Weibull distribution, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist and the closed form expressions of the Bayes estimators cannot be obtained.
In this study, we assume that the scale and shape parameters have the exponential prior and they are independently distributed. We use the Lindley approximation and the Markov Chain Monte Carlo (MCMC) method to obtain the approximate Bayes estimators. In simulation study we compare the effectiveness of the parameter estimation methods with Monte Carlo simulations.

Keywords

Weibull distribution, bayes estimator, lindley approximation, Monte Carlo simulation, MCMC

References

• [1] Hossain. A. And Howlader, H. A. (1996). Unweighted least squares estimation of Weibull parameters. Journal of Statistical Computation and Simulation, 54, 265-271.
• [2] Ahmed, Al O. M., Al-Kutubi, H. S. and Ibrahim, N. A. (2010). Comparison of the Bayesian and Maximum Likelihood Estimation for Weibull Distribution, Journal of Mathematics and Statistics 6 (2): 100-104.
• [3] Hossain, M. A and Zimmer, W. J. (2003). Comparison of Estimation Methods for Weibull Parameters: Complete and Censored Samples, Journal of Statistical Computation and Simulation, Vol. 73(2), pp. 145-153.
• [4] Cox, D. R. And Oakes, D. (1984). Analysis of Survival Data. Chapman and Hall, London.
• [5] Lawless, J. F. (1982). Statistical Models and Methods for Life Time Data. John Wiley and Sons, New York.
• [6] Soland, R. M, (1969). Bayesian Analysis Of The Weibull Process With Unknown Scale And Shape Parameters, IEEE Transactions On Reliability, Vol. R- 18 No. 4, 181-184.
• [7] Guure, C. B. and Ibrahim, N. A.(2013). Methods for Estimating the 2-Parameter Weibull Distribution with Type-I Censored Data, Research Journal of Applied Sciences, Engineering and Technology 5(3): 689-694.
• [8] Kundu, D., Mitr, D. (2016). Bayesian Inference of Weibull Distribution Based on Left Truncated and Right Censored Data, Computational Statistics & Data Analysis, Volume 99, July 2016, Pages 38-50.
• [9] Tsokos, C. P. (1972), “Bayesian approach to reliability: theory and simulation”, in Ann. Reliab. and Maintain. Symp., San Francisco, pp. 78-87
• [10] Papadopoulos, A. S. and Tsokos, C.P. (1976). Bayesian analysis of the Weibull failure model with unknown scale and shape parameters, Statistica, XXXVI, NO. 4, Oct.-Dec.
• [11] Banerjee, A. and Kundu, D. (2008). Inference Based on Type-II Hybrid Censored Data From a Weibull Distribution, IEEE Trans. Reliab., Vol. 57. No. 2, pp. 369-378, Ju.
• [12] Babacan, E. K., Kaya, S. (2019). A Simulation Study of the Bayes Estimator for Parameters in Weibull Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., Volume 68, Number 2, Pages 1664.1674 (2019), Doi: 10.31801/cfsuasmas.455276.
• [13] Kundu, D. (2008). Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring, Technometrics 50 (2) pp. 114-154, May.
• [14] Lindley, D. (1980). Approximate Bayes Methods, University College London.
• [15] Singhl, R., Singh, S. K., Singh, U., Singh, G.P. (2008). Bayes estimator of generalized-exponential Parameters Under Linex Loss Function Using Lindley’s Approximation, Data Science Journal, Volume 7.
• [16] Sultan S. K., Alsadat H. N., Kundu. D. (2014), Bayesian and Maximum Likelihood Estimations of the Inverse Weibull Parameters Under Progressive Type-II Censoring, Journal of Statistical Computation and Simulation, Volume 84, Issue 10,2248–2265.
• [17] Stevyers, M. (2015). Advanced Matlab: Exploratory Data Analysis and Computational Statistics, Course Book.
• [18] Andrews, D. F., Herzberg, A. M. (1985). Data: A Collection of Problems from Many Fields for the Student and Research Worker. New York: Springer Series in Statistics.
• [19] Cooray, K., Ananda, M. M. (2008). A generalization of the half-normal distribution with applications to lifetime data. Communications in Statistics-Theory and Methods, 37(9), 1323-1337.
• [20] Paranaiba, P. F., Ortega, E. M., Cordeiro, G. M., Pascoa, M. A. D. (2013). The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 83(11), 2117-2143.