Definition of Two Self-weights for Continuous Random Variable and Their Applications in Basic Statistics
OwnerLigong Cheninventor
Life of this patent
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Abstract
This invention is for how to define two self-weights for continuous random variable based on sampling, how to SAC-normalize a skewed sampling distribution of a continuous random variable without changing the structure of the original measurement scale of the continuous random variable, how to infer representativeness of mathematical mean, and how to take the advantage of the two self-weights to do t-tests in a two-population comparison.
Claims16
The measurements of the two self-weights, convex self-weight (denoted by C{ci}) and concave self-weight (denoted by R{ri}), defined for each random sample point xi of an original continuous random variable X to describe central tendency and dispersive tendency of the point xi in a sampling distribution, as shown in the computation framework in Table 1 based on the formulas from (7) to (19).
The measurements of sampling errors defined in the formulas (28) and (30) with all the self-weights for the expectation estimate xc of the whole distribution of the original X{xi}.
The measurements of deviations based on the approach of “segmentation-and-combination” for data manipulation that will be claimed in the following claim 10 and claim 11 and defined in the formulas (31), (33), (34) and (36) with all the self-weights defined only in the claim 1 for the two half-distributions of the original random variable X{xi}.
The measurement of an asymmetrical normal range based on the approach of “segmentation-and-combination” for data manipulation that will be claimed in the following claim 10 and defined in the formulas (37) and (38) for the whole distribution of the original X{xi} with all the self-weights defined only in the claim 1 for the expectation estimate xc in the two half-distributions of the original random variable X{xi}.
The measurements of sampling errors based on the approach of “segmentation-and-combination” for data manipulation that will be claimed in the following claim 10 and defined in the formulas (39), (41), (42) and (44) with all the self-weights defined only in the claim 1 for the expectation estimate xc in the two half-distributions of the original random variable X{xi}.
The measurement of an asymmetrical confidence interval based on the approach of “segmentation-and-combination” for data manipulation that will be claimed in the following claim 10 and defined in the formulas (45) and (46) for the whole distribution of the original X{xi} with the self-weights defined only in the claim 1.
The SAC normalization based on the segmentation-and-combination” with the formulas from (47) to (53) and formula (56) as it has been described from the sub-section 5 to the sub-section 8 in the section DETAILED DESCRIPTION and as shown in the FIG. 7, to construct two symmetrically distributed pseudo samples and a size-doubled symmetrically distributed pseudo sample based on the expectation estimated in the arithmetical mean x to replace the xc in the formulas only mentioned in this claim for the original random variable X{xi}.
Any equivalent transformation in a mathematical deduction that may lead to the same computation result(s) of any formula that is claimed in the above claims from 1 to 14 for the same real sample.
Dependencies are inferred from the claim text.