三種三維常態分布之間的最大概似比檢定;Maximum likelihood ratio tests for three trivariate normal distributions

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/84326

Title:	三種三維常態分布之間的最大概似比檢定;Maximum likelihood ratio tests for three trivariate normal distributions
Authors:	許平 Hsu, Ping
Contributors:	數學系
Keywords:	常態分布;最大概似比檢定
Date:	2020-07-14
Issue Date:	2020-09-02 19:05:07 (UTC+8)
Publisher:	國立中央大學
Abstract:	考慮三個三維常態分布 N(u1, E1), N(u2, E2) 及 N(u3, E3),令 (X1,...,Xn) 表一樣本, 其中 Xk = (??1k , ??2k , ??3k ), k = 1,...,n. 並且 N(u2, E2) 為 N(u1, E1) 之特例, N(u3, E3) 為N(u2, E2) 之特例. 本文討論下列三個問題之最大概似比檢定. 問題A H0 ? (X1, ... , Xn ) ~ N(u2, E2) vs H1 : (X1, ... , Xn ) ~ N(u1, E1) 問題B H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u1, E1) 問題C H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u2, E2); Consider three trinormal distributions N(u1, E1), N(u2, E2) and N(u3, E3). Let (X1,...,Xn ) be a sample, where Xk = (??1k , ??2k , ??3k ), k = 1,...,n. Since N(u3, E3), N(u2, E2) and N(u1, E1) are nested, it is interesting to discuss the following three generalized likelihood ratio tests. Problem A H0 ? (X1, ... , Xn ) ~ N(u2, E2) vs H1 : (X1, ... , Xn ) ~ N(u1, E1) Problem B H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u1, E1) Problem C H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u2, E2)
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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