統計的動差，動差母函數和特徵函數之研究

Research of Moment, the Moment-Generating Function and the Characteristic Function of Statistics

羅紹皓(Shao-Hao Lo)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2018年)

https://doi.org/10.6840/cycu201800133

摘要

本論文主要針對大學部的課程中-動差母函數去研究。我們知道一個隨機變數所有動差都有限，但其動差母函數不一定存在。在一般統計原文書中，都有提到要在怎樣的充分條件之下，動差母函數才會存在。但是在坊間或補習班，對於此部分的題目都有錯誤的概念和解法。因此，我們將做一些探討，並整理出各式各樣的條件下，動差母函數才會存在，給讀者們做為參考。

關鍵字

動差 ； 動差母函數 ； 特徵函數

並列摘要

The moment-generating function and the characteristic function of statistics become an important issue. However, previous research on the moment-generating function and the characteristic function of statistics are limited. As we know that all the moments of random variable are finite,but the moment-generation may not necessarily exist. Moreover, there are some wrong concept and misunderstanding solution of the moment-generating function. For the reason, this research tries to synthesize and explore more about the moment-generating function that use the statistical methods to give some new insights.

並列關鍵字

Moment ； Moment-Generating Function ； Characteristic Function

參考文獻

1. Rudin, Walter (1976) Principles of Mathernatical analysis Mcgraw-Hill 3rd New York.。

2. Durrett, Rick (2005) Probability Throry and Examples 3rd Thomson Brooks / Cole U.S.A.。

3. Williams, David (1999) probability with Martingales, Cambridge Mathematical Textbooks.。

4. Casella G. and Roger L.B. (2002) statistical Inference, 2nd

DuXbury Advanced series.。