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論文名稱 Title |
用一個遞迴公式來計算分位數之泰勒多項式 A recursive formula for computing Taylor polynomial of quantile |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
9 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2004-05-28 |
繳交日期 Date of Submission |
2004-06-28 |
關鍵字 Keywords |
分位數、泰勒多項式、生成隨機變數、逆對應法、機率密度函數、遞迴公式、常態分佈 Taylor polynomial, generate random variable, normal distribution, recursive formula, probability density function, inverse transform method, quantile |
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統計 Statistics |
本論文已被瀏覽 5711 次,被下載 3582 次 The thesis/dissertation has been browsed 5711 times, has been downloaded 3582 times. |
中文摘要 |
這篇文章提出一個簡單的遞迴公式來計算連續隨機變數的分位數之泰勒多項式。它可以在一般具有符號計算功能的數學軟體中輕易地執行這個公式,例如Mathematica (Wolfram, 2003)。這裡舉標準常態分佈和生成有界連續分佈的隨機變數的例子來說明。 |
Abstract |
This paper presents a simple recursive formula to compute the Taylor polynomial of quantile for a continuous random variable. It is very easy to implement the formula in standard symbolic programming system, for example Mathematica (Wolfram, 2003). Applications of the formula to standard normal distribution and to the generation of random variables for continuous distribution with bounded support are illustrated. |
目次 Table of Contents |
Abstract........................ ii 1.Introduction.................. 1 2.Examples...................... 3 3.Summary....................... 5 References...................... 7 Appendix........................ 8 |
參考文獻 References |
Dette, H., Melas, V.B. and Pepelyshev, A. (2004). Optimal designs for estimating individual coefficients-a functional approach. J. Statist. Plann. Inference 118, 201-219. Devroye, L. (1986). Non-uniform Random Variate Generation. Springer-Verlag. Kennedy, W.J. and Gentle, J.E. (1980). Statistical Computing. M. Dekker. Ross, S. (2002). Simulation, 3rd edition. Academic Press. Thisted, R.A. (1988). Elements of Statistical Computing:Numerical Computation. CRC Press. Wolfram, S. (2003). The Mathematica Book, 5th edition. Wolfram Media/Cambridge University Press. |
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