The views expressed here are those of the individual authors and not necessarily those of the JSM sponsors, their officers, or their staff.
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
|
The address information is for the authors that have a + after their name.
Authors who are presenting talks have a * after their name.
Back to the full JSM 2011 program
|
2011 JSM Online Program Home
For information, contact jsm@amstat.org or phone (888) 231-3473.
If you have questions about the Continuing Education program, please contact the Education Department.