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Asymptotic Predictive Inference of Negative Lower Tail Index Distributions

  • Amany E. Aly
Published/Copyright: October 7, 2023
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ABSTRACT

In this paper, the results of El-Adll et al. [Asymptotic prediction for future observations of a random sample of unknown continuous distribution, Complexity 2022 (2022), Art. ID 4073799], are extended to the lower negative tail index distributions. Three distinct estimators of the lower negative tail index are proposed, as well as an asymptotic confidence interval. Moreover, different asymptotic predictive intervals for future observations are constructed for distributions attracted to the lower extreme value distribution with a negative tail index. Furthermore, the asymptotic maximum likelihood estimator (AMLE) of the shape parameter, as well as an asymptotic maximum likelihood predictor (AMLP), are obtained. Finally, extensive simulation studies are conducted to demonstrate the efficiency of the proposed methods.

2020 Mathematics Subject Classification: Primary 60G70; 62E20; 62F10; Secondary 62G30; 62G32; 62N05

(Communicated by Gejza Wimmer)


Acknowledgement.

The author is grateful to Professor Gejza Wimmer and the reviewers for their many valuable comments, which improved the presentation of the paper substantially.

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Received: 2022-07-17
Accepted: 2022-10-26
Published Online: 2023-10-07

© 2023 Mathematical Institute Slovak Academy of Sciences

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