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Maximum Likelihood Estimation of the Parameters of Exponentiated Generalized Weibull Based on Progressive Type II Censored Data
Pan African University Institute of Science, Technology and Innovation, Nairobi, Kenya
Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Department of Mathematics, University of Ouagadougou, Ouagadougou, Burkina Faso
Department of Mathematics, University of Potsdam, Potsdam, Germany
- 1 Pan African University Institute of Science, Technology and Innovation, Nairobi, Kenya
- 2 Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
- 3 Department of Mathematics, University of Ouagadougou, Ouagadougou, Burkina Faso
- 4 Department of Mathematics, University of Potsdam, Potsdam, Germany
Open Journal of Statistics·Volume 07 (2017)·Pages 956–963·Published 15 November 2017·DOI10.4236/ojs.2017.76067
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Abstract
Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.
KeywordsMaximum LikelihoodType II Censored DataExponentiated Generalized WeibullEM-Algorithm
- Fréchet (1928) Sur la loi de probabilité de l'écart maximum. Annales de la societe Polonaise de Mathematique, 6, 93-116
- Rosin, P. and Rammler, E. (1933) The Laws Governing the Fineness of powdered coal. Journal of the Institute of Fuel, 7, 29-36.
- Mudhokar, G.S. and Srivastava, D.K. (1993) Exponentiated Weibull Familly for Analysing Bathtub Failure-Rate Data. IEEE Transaction on Reliability, 42, 299-302. https://doi.org/10.1109/24.229504
- Zhang, T. and Xie, M. (2011) On the Upper Truncated Weibull Distribution and Its Reliability Implications. Reliability Engineering and System Safety, 96, 194-200. https://doi.org/10.1016/j.ress.2010.09.004
- Soumaya, G. and Soufiane, G. (2014) Parameters Estimations for Some Modification of the Weibull Distribution. Open Journal of Statistics, 4, 597-610. https://doi.org/10.4236/ojs.2014.48056
- Cordeiro, G.M. Ortega, E.M. and Da Cunha, D.C. (2013) The Exponentiated Generalised Class of Distributions. Journal of Data Science, 11, 127.
- Lehman, E.L. (1953) The Power of Rank Tests. The Annals of Mathematical Statistics, 24, 23-43. https://doi.org/10.1214/aoms/1177729080
- Oguntunde, P., Odetunmibi, O. and Adejumo, A. (2015) On the Exponentiated Generalized Weibull Distribution: A Generalization of the Weibull Distribution. Journal of Science and Technology, 8, 1-7.
- Ng, H.K.T., Chan, P.S. and Balakrishnan, N. (2002) Estimation of Parameters from Progressively Censored Data Using EM Algorithm. Computational Statistics & Data Analysis, 39, 371-389. https://doi.org/10.1016/S0167-9473(01)00091-3
- Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B, 1-38.
- Balakrishnan, N. and Sandhu, R. (1995) A Simple Simulational Algorithm for Generating Progressive Type II Censored Samples. The American Statistician, 49, 229-230.