EFFICIENT BOUNDS FOR SCALE AND THRESHOLD PARAMETERS IN THE CASE OF THE THREE-PARAMETER WEIBULL DISTRIBUTION
Bounds of location and scale parameters of three-parameter Weibull distribution are proposed in this paper. These bounds are data dependent and are therefore adaptive. Exact probabilities of recovery of the parameters concerned were proposed and then applied to simulated data.
Weibull distribution, parameter range, order statistic, bounds of parameters.
Received: September 4, 2021; Accepted: October 25, 2021; Published: November 15, 2021
How to cite this article: Jean-Etienne O. Ouédraogo, Edoh Katchekpele and Frederic Bere, Efficient bounds for scale and threshold parameters in the case of the three-parameter Weibull distribution, Far East Journal of Theoretical Statistics 63(1) (2021), 19-28. DOI: 10.17654/TS063010019
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] S. Acitas, C. H. Aladag and B. Senoglu, A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: an application to the strengths of glass fibre data, Reliability Engineering and System Safety 183(C) (2019), 116-127.[2] B. Bobee and F. Ashkar, The Gamma Family and Derived Distributions Applied in Hydrology, Water Resources Publications, 1991.[3] G. Casella and C. P. Robert, Introducing Monte Carlo Methods with R, Springer, New York, NY, 2010.[4] R. C. H. Cheng and T. C. Iles, Embedded models in three-parameter distributions and their estimation, J. Roy. Statist. Soc. Ser. B 52(1) (1990), 135-149.[5] R. C. H. Cheng and T. C. Iles, Corrected maximum likelihood in non-regular problems, J. Roy. Statist. Soc. Ser. B 49(1) (1987), 95-101.[6] C. A. Cohen and B. Whitten, Modified maximum likelihood and modified moment estimators for the three-parameter Weibull distribution, Comm. Statist. Theory Methods 11(23) (1982), 2631-2656.[7] A. D. Griffiths, Interval estimation for the three-parameter lognormal distribution via the likelihood function, J. Roy. Statist. Soc. Ser. C 29(1) (1980), 58-68.[8] H. Hirose, Maximum likelihood estimation in the 3-parameter Weibull distribution, A look through the generalized extreme-value distribution, IEEE Trans. Dielectr. Electr. Insul. 3 (1996), 43-55.[9] H. Nagatsuka, T. Kamakura and N. Balakrishnan, A consistent method of estimation for the three-parameter Weibull distribution, Comput. Statist. Data Anal. 58 (2013), 210-226.[10] L. J. Norman, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, 2nd ed., Vol. 1, John Wiley and Sons, New York, 1994.[11] H. H. Örkcü, O. V. Soner, A. Ertugrul and M. I. Dogan, Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: a comprehensive experimental comparison, Appl. Math. Comput. 268 (2015), 201-226.[12] J. E. O. Ouédraogo, B. Some and S. Dossou-Gbete, On maximum likelihood estimation for the three-parameter Gamma distribution based on left censored samples, Science Journal of Applied Mathematics and Statistics 5 (2017), 147-163.[13] J.-E. O. Ouédraogo, E. Katchekpele and S. Tiendrebeogo, Alienor’s approach for the Pearson type 3 parameters estimation, Far East J. Appl. Math. 108(1) (2020), 67-80.[14] H. Z. Qiao and C. P. Tsokos, Estimation of the three-parameter Weibull probability distribution, Math. Comput. Simulation 39 (1995), 173-185.[15] R Core Team, R: A language and environment for statistical computing, 2015. http://www.R-project.org/.[16] R. L. Smith, Maximum likelihood estimation in a class of nonregular cases, Biometrika 72(1) (1985), 67-90.[17] W. Xu, Y.-X. Xue, G.-X. Shen and Y.-Z. Zhang, Parameter estimation of three-parameter Weibull distribution via particle swarm optimization algorithm, Proceedings 2011 International Conference on Transportation, Mechanical, and Electrical Engineering (TMEE), 2011, pp. 336-338.[18] F. Yang, H. Ren and Z. Hu, Maximum likelihood estimation for three-parameter Weibull distribution using evolutionary strategy, Math. Probl. Eng. 2019, Art. ID 6281781, 1-8.