Weighted variance

In the case of an nxp matrix X we can define two sets of weighted measures of location and spread, one for each of the two dual spaces and in terms of weighted means and weighted variances ... 

When feature selection is used to simplify, because of the large number of variables, methods must be simple. The univariate criterion of interclass variance/intraclass variance ratio (in the different variants called Fisher weights variance weights or Coomans weights is simple, but can lead to the elimination of variables with some discriminant power, either separately or, more important, in connection with other variables (Fig. 36). 

The material obtained from the kneading process should be, after drying and blending, compressed to tablets. The compressing capabilities and the tablet characteristics (content uniformity, thickness, hardness, friability, weight variances, and disintegration time) should meet the finished product specification for the compressed tablets. 

The relative second moment, K2 jF, a dimensionless quantity, is a measure of polydispersity. It is the intensity-weighted variance divided by the square of the intensity-weighted average of the diffusion coefficient distribution. The relative second moment is also called the polydispersity... 

Weighted variance. A weighted measure of variance, defined as... 

To weight variances changing at the different observation points x, a weight based on the reciprocal standard deviation (variance) could be applied ... 

We ran the previous tests using simply weighted variance-covariance matrices. This means that each piece of data was equally weighted when constructing the matrix. For instance, we gave the 1-year gilt rate on 31 January 2001 the same consideration as the one on 30 April 2002. In order to compensate for recent changes in volatility of the various fac-... 

One may assume that features with a great variance are more important for a classification than features with a small variance. For a class-independent weighting, variance v of feature i is given by equation (95). 

If all Ns particles are equally likely to be selected in acquisition of the primary sample, the particles are referred to (Heydorn 2004) as sampling units and then hj has a mean value of zero (by definition) and a weighted variance Vsu given by ... 

Factor 1 can be named as Technology and Measurements of Exposure , Factor 2 as Management and Guidance , Factor 3 as Monitoring and Factors 4 as Risk Management . Weighted variances explained by each factor are as follows Factor 1 —18 %, Factor 2—15 %, Factor 3—14 %, Factor 4—12 %. 

One of the most difficult tasks in using PCR and PLS is determining the correct number of loading vectors (factors) to use to model the data. As more and more vectors are calculated, they are ordered by the degree of importance to the model (either by variance in PCA or concentration weighted variance in PLS). Eventually, the loading vectors will begin to model the system noise (which usually provides the smallest contribution to the data). 

Of course, such a large difference could happen by chance, by the statistical roll of the dice, but it is more likely that there are other sources of uncertainty in addition to that due to counting and not accounted for in the uncertainty quoted. We could, of course, simply ignore the uncertainties on the individual values and calculate a simple mean. That, however, would not take into account the relative degrees of reliability of the individual values. In such cases, a standard deviation derived from the weighted variance might be quoted, calculated as follows ... 

It is possible to weight variances in such a way that F will be 1. Therefore, WE must be calculated from ... 

Sample Variance n The uniformly weighted variance of the elements in the sample with respect to the sample mean. For a sample, X, consisting of Xj, X2,. .. the sample mean would be given by ... 

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