American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
Go
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 33-48
DOI: 10.12691/ajams-5-2-1
Open AccessReview Article

Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes

Ahmed Elshahhat1,

1Department of Accounting & Quantitative Information Systems, Faculty of Technology & Development, Zagazig University, Egypt

Pub. Date: April 11, 2017

Cite this paper:
Ahmed Elshahhat. Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes. American Journal of Applied Mathematics and Statistics. 2017; 5(2):33-48. doi: 10.12691/ajams-5-2-1

Abstract

Based on Type-I and Type-II generalized progressive hybrid censoring schemes, the maximum likelihood estimators and Bayes estimators for the unknown parameters of exponentiated Weibull lifetime model are derived. The approximate asymptotic variance-covariance matrix and approximate confidence intervals based on the asymptotic normality of the classical estimators are obtained. Independent non-informative types of priors are considered for the unknown parameters to develop the Bayes estimators and corresponding Bayes risks under a squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. Finally, one real data set is analyzed for illustrative purposes.

Keywords:
asymptotic variance-covariance matrix Bayes estimator confidence interval exponentiated Weibull distribution generalized progressive hybrid censoring schemes maximum likelihood estimator squared error loss function

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Ashour, S. & Elshahhat, A. (2016). Bayesian and non-Bayesian estimation for Weibull parameters based on generalized Type-II progressive hybrid censoring scheme. Pakistan Journal of Statistics & Operation Research, 12(2), 213-226.‏
 
[2]  Childs, A., Chandrasekar, B. & Balakrishnan, N. (2008). Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In Statistical Models and Methods for Biomedical and Technical Systems, Vonta, F., Nikulin, M., Limnios, N. & Huber-Carol, C, (Eds), Birkhäuser, Boston, 319-330.
 
[3]  Cho, Y., Sun, H., & Lee, K. (2015a). Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy, 17(1), 102-122.‏
 
[4]  Cho, Y., Sun, H., & Lee, K. (2015b). Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme. Statistical Methodology, 23, 18-34.‏
 
[5]  Cohen, A. C. (1965). Maximum likelihood estimation in the Weibull distribution based on complete and censored samples. Technometrics, 7(4), 579-588.
 
[6]  Kundu, D. & Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics & Data Analysis, 50(10), 2509-2528.
 
[7]  Lee, K., Sun, H., & Cho, Y. (2016a). Exact likelihood inference of the exponential parameter under generalized Type-II progressive hybrid censoring. Journal of the Korean Statistical Society, 45(1), 123-136.‏
 
[8]  Lee, K. J., Lee, J. I., & Park, C. K. (2016b). Analysis of generalized progressive hybrid censored competing risks data. Journal of the Korean Society of Marine Engineering, 40(2), 131-137.‏
 
[9]  Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42(2), 299-302.‏
 
[10]  Mudholkar, G. S., Srivastava, D. K., & Freimer, M. (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics, 37(4), 436-445.‏
 
[11]  Mudholkar, G. S., & Hutson, A. D. (1996). The exponentiated Weibull family: some properties and a flood data application. Communications in Statistics-Theory & Methods, 25(12), 3059-3083.‏
 
[12]  Nassar, M. M., & Eissa, F. H. (2003). On the exponentiated Weibull distribution. Communications in Statistics-Theory & Methods, 32(7), 1317-1336.‏
 
[13]  Nichols, M. D., & Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles. Quality & Reliability Engineering International, 22(2), 141-151.‏
 
[14]  Singh, U., Gupta, P. K., & Upadhyay, S. K. (2005). Estimation of three-parameter exponentiated-Weibull distribution under Type-II censoring. Journal of Statistical Planning & Inference, 134(2), 350-372.‏