三獨立常態樣本變異數間之順序的機率(III); Probability of orders between three independent normal sample variances(III)

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/60131

Title:	三獨立常態樣本變異數間之順序的機率(III);Probability of orders between three independent normal sample variances(III)
Authors:	賴俊儒;Lai,CHun-Ju
Contributors:	數學系
Keywords:	獨立常態;樣本變異數順序;機率
Date:	2013-06-24
Issue Date:	2013-07-10 12:07:42 (UTC+8)
Publisher:	國立中央大學
Abstract:	令S^2_{x n}, S^2_{y n} 及S^2_{z n} 分表取自N( x \sigma ^ 2_x), N( y \sigma ^2_y) 及N( z \sigma ^ 2_z )之樣本變異數.當 n 為不小於 2 之整數時, 謝宗翰(2012)計算P(S^2_{x n} > S^2_{y n}) 之值, 當 n 為不小於 3 之奇數時, 謝宗翰(2012)計算P(S^2_{x n} > S^2_{y n} > S^2_{z n}) 之值. 本文用不同的方式來計算P(S^2_{x n} > S^2_{y n}) 及P(S^2_{x n} > S^2_{y n} > S^2_{z n}), 其結果均適用於不小於 2 之整數 n . Let S^2_{x n}, S^2_{y n} and S^2_{z n} denote sample variances obtained from three independent normal distributions. Each sample has sample size n. Shieh(2012) calculated P(S^2_{x n} > S^2_{y n}) when n > = 2 and P(S^2_{x n} > S^2_{y n} > S^2_{z n)} when n >= 3 is odd. In this paper, we calculate P(S^2_{x n} > S^2_{y n}) and P(S^2_{x n} > S^2_{y n} > S^2_{z n}) by di erent methods and the results are valid for n 2.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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