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博碩士論文 etd-0628104-154820 詳細資訊
Title page for etd-0628104-154820
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
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
9
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
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
統計
Statistics
本論文已被瀏覽 5711 次,被下載 3582
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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