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Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Arts and Sciences Faculty, Statistics Department, University of Kirikkale, Kirikkale 71450, Turkey
Entropy 2019, 21(5), 451; https://doi.org/10.3390/e21050451
Received: 31 January 2019 / Revised: 19 April 2019 / Accepted: 26 April 2019 / Published: 30 April 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
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Abstract

In the modeling of successive arrival times with a monotone trend, the alpha-series process provides quite successful results. Both selecting the distribution of the first arrival time and making an optimal statistical inference play a crucial role in the modeling performance of the alpha-series process. In this study, when the distribution of the first arrival time is the generalized Rayleigh, the problem of statistical inference for the α , β , and λ parameters of the alpha-series process is considered. Further, in order to obtain optimal modeling performance from the mentioned alpha-series process, various estimators for the model parameters are obtained by employing different estimation methodologies such as maximum likelihood, modified maximum spacing, modified least-squares, modified moments, and modified L-moments. By a series of Monte Carlo simulations, the estimation efficiencies of the obtained estimators are evaluated through the different sample sizes. Finally, two real datasets are analyzed to illustrate the importance of modeling with the alpha-series process. View Full-Text
Keywords: alpha-series process; geometric process; maximum likelihood estimate; modified maximum spacing estimate; modified least-squares estimate alpha-series process; geometric process; maximum likelihood estimate; modified maximum spacing estimate; modified least-squares estimate
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Demirci Biçer, H. Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution. Entropy 2019, 21, 451.

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