JSM 2011 Online Program

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Abstract Details

Activity Number: 43
Type: Contributed
Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #300638
Title: A New Horizon of Statistics: The Definition of Self-Weight for Continuous Variattribute (=Continuous Random Variable, CRV)
Author(s): Ligong Chen and Yongmei Chen*+
Companies: USUHS , USUHS and USUHS
Address: Center for Prostate Diseases Research, Rockville, MD, 20852,
Keywords: Continuous Random Variable ; Self-weight ; Self-weighted Mean ; Self-weighted Deviation ; Sampling Error of the Self-weighted Mean ; Representativeness of Arithmetical Mean
Abstract:

A CRV X and its n random points x_i can be expressed in X{x_i}(i=1,2,.,n). We define a point-to-point differentiality D_j(j=i) with its range R_X for x_i as D_j{d_ij}=|X-x_i|/R_X and a similarity S_j{s_ij}=1-D_j{d_ij}. A product V{v_i} of the sum of D_j and the sum of S_j will be a real measure in a range R_V. We define C{c_i}=1-[V-min(V)]/R_V as an unbiased self-weight for the X{x_i} to the E(X). Then, we will have a convex-concave self-weight curve, i.e. it looks like a normal curve if the X is normal. Based on examining two properties of sample size n, we tried to unify the definitions of the weighted and non-weighted basic statistics, in which the degree of freedom may be defined as the sum of weights minus the self-weighted mean of the weight. These unified definitions can be used to substitute various optimizations in advanced statistical methodological constructions. We also tried


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