On the comparison of Fisher information of the Weibull and GE distributions |
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| Institution: | 1. Department of Computer Science and Statistics, The University of New Brunswick at Saint John, New Brunswick, Canada E2L 4L5;2. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India;1. Department of Industrial Engineering, Pusan National University, Busan 46241, Republic of Korea;2. Statematics Consulting, 4 Sylvan Terrace, New York, NY 10032, USA;1. Applied Statistics Laboratory, Department of Industrial Engineering, Pusan National University, Busan 46241, Republic of Korea;2. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, China;3. Department of Management Science and Statistics, University of Texas at San Antonio, San Antonio, TX 78249, USA |
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| Abstract: | In this paper, we consider the Fisher information matrices of the generalized exponential (GE) and Weibull distributions for complete and Type-I censored observations. Fisher information matrix can be used to compute asymptotic variances of the different estimators. Although both distributions may provide similar data fit but the corresponding Fisher information matrices can be quite different. Moreover, the percentage loss of information due to truncation of the Weibull distribution is much more than the GE distribution. We compute the total information of the Weibull and GE distributions for different parameter ranges. We compare the asymptotic variances of the median estimators and the average asymptotic variances of all the percentile estimators for complete and Type-I censored observations. One data analysis has been preformed for illustrative purposes. When two fitted distributions are very close to each other and very difficult to discriminate otherwise, the Fisher information or the above mentioned asymptotic variances may be used for discrimination purposes. |
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