Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues
Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. In this note an O(N3) algorithm is developed for computing the probabilit...
| Main Authors: | , |
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| Format: | Working Paper |
| Language: | en_US |
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Massachusetts Institute of Technology, Operations Research Center
2004
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/5159 |
| _version_ | 1811094107286667264 |
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| author | Jones, Lee K. Larson, Richard C., 1943- |
| author_facet | Jones, Lee K. Larson, Richard C., 1943- |
| author_sort | Jones, Lee K. |
| collection | MIT |
| description | Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. In this note an O(N3) algorithm is developed for computing the probability that the order statistics vector lies in a given rectangle. The new algorithm is then applied to a problem of statistical inference in queues. Illustrative computational results are included. |
| first_indexed | 2024-09-23T15:55:12Z |
| format | Working Paper |
| id | mit-1721.1/5159 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:55:12Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/51592019-04-12T08:06:51Z Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues Jones, Lee K. Larson, Richard C., 1943- Order statistics, queues, statistical inference, queue inference engine. Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. In this note an O(N3) algorithm is developed for computing the probability that the order statistics vector lies in a given rectangle. The new algorithm is then applied to a problem of statistical inference in queues. Illustrative computational results are included. 2004-05-28T19:25:46Z 2004-05-28T19:25:46Z 1991-05 Working Paper http://hdl.handle.net/1721.1/5159 en_US Operations Research Center Working Paper;OR 249-91 487497 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Order statistics, queues, statistical inference, queue inference engine. Jones, Lee K. Larson, Richard C., 1943- Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues |
| title | Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues |
| title_full | Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues |
| title_fullStr | Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues |
| title_full_unstemmed | Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues |
| title_short | Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues |
| title_sort | efficient computation of probabilities of events described by order statistics and application to a problem of queues |
| topic | Order statistics, queues, statistical inference, queue inference engine. |
| url | http://hdl.handle.net/1721.1/5159 |
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