Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics
In this paper, a new definition of the number of observations near the kth order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2020/4262574 |
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| _version_ | 1832546820665901056 |
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| author | Masoumeh Akbari |
| author_facet | Masoumeh Akbari |
| author_sort | Masoumeh Akbari |
| collection | DOAJ |
| description | In this paper, a new definition of the number of observations near the kth order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions xn,0<x<1,n≥1. Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations. |
| format | Article |
| id | doaj-art-93782089678849cdbb8c665371f82e81 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-93782089678849cdbb8c665371f82e812025-02-03T06:47:05ZengWileyJournal of Probability and Statistics1687-952X1687-95382020-01-01202010.1155/2020/42625744262574Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order StatisticsMasoumeh Akbari0Department of Statistics, University of Mazandaran, Babolsar, Mazandaran, IranIn this paper, a new definition of the number of observations near the kth order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions xn,0<x<1,n≥1. Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.http://dx.doi.org/10.1155/2020/4262574 |
| spellingShingle | Masoumeh Akbari Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics Journal of Probability and Statistics |
| title | Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics |
| title_full | Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics |
| title_fullStr | Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics |
| title_full_unstemmed | Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics |
| title_short | Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics |
| title_sort | characterization and goodness of fit test of pareto and some related distributions based on near order statistics |
| url | http://dx.doi.org/10.1155/2020/4262574 |
| work_keys_str_mv | AT masoumehakbari characterizationandgoodnessoffittestofparetoandsomerelateddistributionsbasedonnearorderstatistics |