Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution
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 pro...
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MDPI AG
2019-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/5/451 |
| _version_ | 1811305149318037504 |
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| author | Hayrinisa Demirci Biçer |
| author_facet | Hayrinisa Demirci Biçer |
| author_sort | Hayrinisa Demirci Biçer |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>, and <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> 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. |
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| id | doaj.art-7e02616e2ef244dda7e3e47e90505a40 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T08:20:19Z |
| publishDate | 2019-04-01 |
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| spelling | doaj.art-7e02616e2ef244dda7e3e47e90505a402022-12-22T02:54:40ZengMDPI AGEntropy1099-43002019-04-0121545110.3390/e21050451e21050451Statistical Inference for Alpha-Series Process with the Generalized Rayleigh DistributionHayrinisa Demirci Biçer0Arts and Sciences Faculty, Statistics Department, University of Kirikkale, Kirikkale 71450, TurkeyIn 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 <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>, and <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> 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.https://www.mdpi.com/1099-4300/21/5/451alpha-series processgeometric processmaximum likelihood estimatemodified maximum spacing estimatemodified least-squares estimate |
| spellingShingle | Hayrinisa Demirci Biçer Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution Entropy alpha-series process geometric process maximum likelihood estimate modified maximum spacing estimate modified least-squares estimate |
| title | Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution |
| title_full | Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution |
| title_fullStr | Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution |
| title_full_unstemmed | Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution |
| title_short | Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution |
| title_sort | statistical inference for alpha series process with the generalized rayleigh distribution |
| topic | alpha-series process geometric process maximum likelihood estimate modified maximum spacing estimate modified least-squares estimate |
| url | https://www.mdpi.com/1099-4300/21/5/451 |
| work_keys_str_mv | AT hayrinisademircibicer statisticalinferenceforalphaseriesprocesswiththegeneralizedrayleighdistribution |