Chi-Square分配與F分配的最小信賴區間之研究

Study Of Minimum Length Of Confidence Interval About Chi-Square Distribution And F Distribution

許載仁(Tsai-Jen Hsu)

指導教授 ： 王國徵

淡江大學/理學院/數學學系碩士班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00729

摘要

本文是探討F分配的最小信賴區間。Crisman在1975年的論文提到可利用二分法來尋找Chi-Square分配的最小信賴區間之臨界值。本篇論文會先探討Crisman的研究，並使用相同的方法探討F分配的最小信賴區間之臨界值，最後提供範例與SAS Macro程式供讀者使用。

關鍵字

信賴區間 ； F分配

並列摘要

This article is to explore the minimum length of confidence interval of F distribution. In 1975, Crisman had mentioned a bisection method to calculate the confidence interval with the minimum length about the Chi-Square distribution to meet the desired critical values. This paper will first explore Crisman’s research and applies the same method on F distribution to find the confidence interval with minimum length, finally we will provide a SAS Macro program and use some examples to illustrate how to use it.

並列關鍵字

Confidence Interval ； F Distribution

參考文獻

[1] Crisman, Roger. "Shortest confidence interval for the standard deviation of a normal distribution." J. Undergrad. Math 7.2 (1975): 57.

[2] Roussas, George. "An Introduction To Probability And Statistical Inference" Academic Press (2003)