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The current attempt is aimed to extend previous results, concerning the explicit expression of the arithmetic mean standard deviation distribution, to the general case of the weighted mean standard deviation distribution. To this respect, the integration domain is expressed in canonical form after a change of reference frame in the n-space, which is recognized as an infinitely thin n-cylindrical corona where the axis coincides with a coordinate axis and the orthogonal section is an infinitely thin, homotetic (n-1)-elliptical corona. The semiaxes are formulated in two different ways, namely in terms of (1) eigenvalues, via the eigenvalue equation, and (2) leading principal minors of the matrix of a quadratic form, via the Jacobi formulae. The distribution and related parameters have the same formal expression with respect to their counterparts in the special case where the weighted mean coincides with the arithmetic mean. The reduction of some results to ordinary geometry is also considered.
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篇名 The Weighted Mean Standard Deviation Distribution: A Geometrical Framework
来源期刊 应用数学(英文) 学科 数学
关键词 Standard Deviation n-Spaces Direction Cosines QUADRATIC FORMS MATRIX Theory
年,卷(期) 2015,(3) 所属期刊栏目
研究方向 页码范围 520-546
页数 27页 分类号 O1
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Standard
Deviation
n-Spaces
Direction
Cosines
QUADRATIC
FORMS
MATRIX
Theory
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应用数学(英文)
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2152-7385
武汉市江夏区汤逊湖北路38号光谷总部空间
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