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The weighted mean in this case is: ¯ = ¯ (=), (where the order of the matrix–vector product is not commutative), in terms of the covariance of the weighted mean: ¯ = (=), For example, consider the weighted mean of the point [1 0] with high variance in the second component and [0 1] with high variance in the first component.
Author-level metrics are citation metrics that measure the bibliometric impact of individual authors, researchers, academics, and scholars. Many metrics have been developed that take into account varying numbers of factors (from only considering the total number of citations, to looking at their distribution across papers or journals using statistical or graph-theoretic principles).
The best-known author-level measures include total citations and the h-index. [16] Each measure has advantages and disadvantages, [17] spanning from bias to discipline-dependence and limitations of the citation data source. [18] Counting the number of citations per paper is also employed to identify the authors of citation classics. [19]
Weighted geometric mean; Weighted least squares This page was last edited on 24 April 2009, at 14:49 (UTC). Text is available under the Creative Commons Attribution ...
Despite the newly abstract situation, this definition is extremely similar in nature to the very simplest definition of expected values, given above, as certain weighted averages. This is because, in measure theory, the value of the Lebesgue integral of X is defined via weighted averages of approximations of X which take on finitely many values ...
Weighted means are commonly used in statistics to compensate for the presence of bias.For a quantity measured multiple independent times with variance, the best estimate of the signal is obtained by averaging all the measurements with weight = /, and the resulting variance is smaller than each of the independent measurements = /.
Like a power mean, a Lehmer mean serves a non-linear moving average which is shifted towards small signal values for small and emphasizes big signal values for big .Given an efficient implementation of a moving arithmetic mean called smooth you can implement a moving Lehmer mean according to the following Haskell code.
Another use of weighting is in television, in which the red, green and blue components of the signal are weighted according to their perceived brightness. This ensures compatibility with black and white receivers and also benefits noise performance and allows separation into meaningful luminance and chrominance signals for transmission.