Interval Estimation in Location-Scale Family, Using Information Measures
Keywords:
Asymptotic confidence interval, location and scale family, Shannon entropy, varentropyAbstract
Interval estimation is one of the important concepts in statistics. There are different methods to find a confidence interval for distribution parameters, but finding an optimal confidence interval is always a concern. On the other hand, it is important to find a confidence interval for the Shannon information of the ith order statistic when the distribution parameters are unknown. In the present paper, using information measures, we introduce an asymptotic confidence interval for scale parameter and the Shannon information of the ith order statistic related to the location-scale family. Via simulation study, we study the coverage probability and length of confidence intervals. Finally, some examples for hypothesis testing related to the Shannon information of the ith order statistic and the scale parameter are provided.
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