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On the comparison of Fisher information of the Weibull and GE distributions. (English) Zbl 1094.62122
Summary: We consider the Fisher information matrices of the generalized exponential (GE) and Weibull distributions for complete and Type-I censored observations. The Fisher information matrix can be used to compute asymptotic variances of the different estimators. Although both distributions may provide similar data fit 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 performed 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.

MSC:
62N01 Censored data models
62F12 Asymptotic properties of parametric estimators
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