UNIQUENESS OF PRINCIPAL POINTS FOR UNIVARIATE DISTRIBUTIONS

被引:26
作者
LI, LN
FLURY, B
机构
[1] NATL CTR ATMOSPHER RES,ADV STUDY PROGRAM,BOULDER,CO 80307
[2] INDIANA UNIV,DEPT MATH,BLOOMINGTON,IN 47405
关键词
PRINCIPAL POINTS; K-MEANS ALGORITHM; NORMAL MIXTURE;
D O I
10.1016/0167-7152(94)00237-3
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
This paper presents a proof of uniqueness of k principal of the univariate normal distributions. A sufficient condition of uniqueness is given, and a normal mixture example is discussed.
引用
收藏
页码:323 / 327
页数:5
相关论文
共 14 条
[1]  
Chow, On the uniqueness of best L<sub>2</sub>[0, 1] approximation by piecewise polynomials with variable breakpoints, Math. Comput., 30, pp. 571-585, (1982)
[2]  
Cox, Note on grouping, Journal of the American Statistical Association, 52, pp. 543-547, (1957)
[3]  
Day, Estimating the components of mixture of normal distributions, Biometrika, 56, pp. 463-474, (1969)
[4]  
Dalenius, The problem of optimum stratification, Skandinavisk Aktuarietidskrift, 33, pp. 203-213, (1950)
[5]  
Dalenius, Gurney, The problem of optimum stratification II, Skandinavisk Aktuarietidskrift, 34, pp. 203-213, (1951)
[6]  
Eubank, Optimal grouping, spacing, stratification, and piecewise constant approximation, SIAM Rev., 30, pp. 404-420, (1988)
[7]  
Flury, Principal points, Biometrika, 77, pp. 33-41, (1990)
[8]  
Flury, Estimation of principal points, Applied Statistics, 42, (1993)
[9]  
Hartigan, Clustering Algorithms, (1975)
[10]  
Pearson, On linear and planes of closest fit to systems of points in space, Philosophical Magazine Series 6, 2, pp. 559-572, (1901)