| 基于前四阶矩的非高斯响应概率密度函数逼近方法研究 |
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| 引用本文： | 叶江水,王仲刚,陈友良,黄高琼.基于前四阶矩的非高斯响应概率密度函数逼近方法研究[J].后勤工程学院学报,2010,26(1):12-16. |
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| 作者姓名： | 叶江水 王仲刚 陈友良 黄高琼 |
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| 作者单位： | 1. 后勤工程学院,军事建筑工程系,重庆,401311
2. 中铁电气化勘测设计研究院有限公司,天津,300250 |
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| 基金项目： | 重庆市自然科学基金资助项目(CSTC,2006BB3127);;2009年度后勤工程学院研究生创新专项经费资助 |
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| 摘 要： | 基于响应前四阶统计矩研究了在偏态系数和峰度系数取值范围不同时Gram-Charlier渐进展式、Edgeworth渐进展式和Fleishman多项式3种非高斯概率密度函数,指出3种方法的适用条件。结果表明与Gram-Charlier和Edgeworth渐进展式相比,Fleishman多项式对峰度系数的变化不敏感,该方法只有在峰度系数与高斯分布一致时拟合的结果才有可能是合理的;Gram-Charlier和Edgeworth渐进展式在中、高度偏态情况下易出现负的概率,二者在低等偏态情况下拟合的结果是比较合理的。两算例表明在高等偏态、尖峰和对称、扁平分布情况下,Gram-Charlier和Edgeworth渐进展式拟合结果优于Fleishman多项式,但Gram-Charlier渐进展式易于出现负的概率,在应用时应引起注意。
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| 关 键 词： | 非高斯 概率密度函数 偏态 峰度 |
Research on Approximate Methods of Non-Gaussian Probability Density Function Based on the First Four Moments of the Response |
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| YE Jiang-shui,WANG Zhong-gang,CHEN You-liang,HUANG Gao-qiong.Research on Approximate Methods of Non-Gaussian Probability Density Function Based on the First Four Moments of the Response[J].Journal of Logistical Engineering University,2010,26(1):12-16. |
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| Authors: | YE Jiang-shui WANG Zhong-gang CHEN You-liang HUANG Gao-qiong |
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| Institution: | 1.Dept.of Architecture & Civil Engineering;LEU;Chongqing 401311;China;2.China Railway Electrification Survey Design & Research Institute Co.;Ltd;Tianjin 300250;China |
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| Abstract: | Based on the first four moments of response,the paper studies three common approximate methods of non-Gaussian probability density function:Gram-Charlier expansion procedure,Edgeworth expansion procedure and Fleishman polynomials.The differences among these methods with different range of skewness coefficient and kurtosis coefficient are analyzed.Their applicable cases are pointed out.The results show that compared with Gram-Charlier and Edgeworth expansion procedures the Fleishman polynomials is not sensit... |
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| Keywords: | non-Gaussian probability density function skewness kurtosis |
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