### Abstract

Generally, we get probability distribution quantile by looking through numerical tables, however, it is not only easy to make mistake, but also limited in precision, no more than 0.0001. And programming techniques up to now are either too restrictive to be applied to general cases, or too complicated to be implemented for practical use. Therefore, there is a need for robust procedures to estimate quantiles, which can be applied to relatively generic processes and easy to implement. The paper briefly discusses the algorithm and the implement of some familiar probability distribution quantiles, such as, standardized normal distribution, β distribution, X^{2} distribution, t distribution and F distribution. Especially, we use Newton dichotomy here to improve the precision, in the case of t and F distributions which is insufficient by approximate formulae only, because of the accumulated error. An experimental performance evaluation demonstrates the validity of these procedures to calculate probability distribution quantiles.

Original language | English (US) |
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Title of host publication | 2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005 |

Pages | 2783-2788 |

Number of pages | 6 |

State | Published - Dec 12 2005 |

Event | International Conference on Machine Learning and Cybernetics, ICMLC 2005 - Guangzhou, China Duration: Aug 18 2005 → Aug 21 2005 |

### Other

Other | International Conference on Machine Learning and Cybernetics, ICMLC 2005 |
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Country | China |

City | Guangzhou |

Period | 8/18/05 → 8/21/05 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005*(pp. 2783-2788)

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*2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005.*pp. 2783-2788, International Conference on Machine Learning and Cybernetics, ICMLC 2005, Guangzhou, China, 8/18/05.

**Computer implementation of probability distribution quantile estimation.** / Yu, Xian Chuan; Yuan, Zhongyi; Yu, Chen; Yang, Meng.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Computer implementation of probability distribution quantile estimation

AU - Yu, Xian Chuan

AU - Yuan, Zhongyi

AU - Yu, Chen

AU - Yang, Meng

PY - 2005/12/12

Y1 - 2005/12/12

N2 - Generally, we get probability distribution quantile by looking through numerical tables, however, it is not only easy to make mistake, but also limited in precision, no more than 0.0001. And programming techniques up to now are either too restrictive to be applied to general cases, or too complicated to be implemented for practical use. Therefore, there is a need for robust procedures to estimate quantiles, which can be applied to relatively generic processes and easy to implement. The paper briefly discusses the algorithm and the implement of some familiar probability distribution quantiles, such as, standardized normal distribution, β distribution, X2 distribution, t distribution and F distribution. Especially, we use Newton dichotomy here to improve the precision, in the case of t and F distributions which is insufficient by approximate formulae only, because of the accumulated error. An experimental performance evaluation demonstrates the validity of these procedures to calculate probability distribution quantiles.

AB - Generally, we get probability distribution quantile by looking through numerical tables, however, it is not only easy to make mistake, but also limited in precision, no more than 0.0001. And programming techniques up to now are either too restrictive to be applied to general cases, or too complicated to be implemented for practical use. Therefore, there is a need for robust procedures to estimate quantiles, which can be applied to relatively generic processes and easy to implement. The paper briefly discusses the algorithm and the implement of some familiar probability distribution quantiles, such as, standardized normal distribution, β distribution, X2 distribution, t distribution and F distribution. Especially, we use Newton dichotomy here to improve the precision, in the case of t and F distributions which is insufficient by approximate formulae only, because of the accumulated error. An experimental performance evaluation demonstrates the validity of these procedures to calculate probability distribution quantiles.

UR - http://www.scopus.com/inward/record.url?scp=28444495970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28444495970&partnerID=8YFLogxK

M3 - Conference contribution

SN - 078039092X

SN - 9780780390928

SP - 2783

EP - 2788

BT - 2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005

ER -