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The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean .
The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis , and are closely related to the concept of a measure .
The idea of the kernel average smoother is the following. For each data point X 0 , choose a constant distance size λ (kernel radius, or window width for p = 1 dimension), and compute a weighted average for all data points that are closer than λ {\displaystyle \lambda } to X 0 (the closer to X 0 points get higher weights).
Data can be binary, ordinal, or continuous variables. It works by normalizing the differences between each pair of variables and then computing a weighted average of these differences. The distance was defined in 1971 by Gower [1] and it takes values between 0 and 1 with smaller values indicating higher similarity.
The inverse-variance weighted average has the least variance among all weighted averages, which can be calculated as (^) = /. If the variances of the measurements are all equal, then the inverse-variance weighted average becomes the simple average. Inverse-variance weighting is typically used in statistical meta-analysis or sensor fusion to ...
It is a measure used to evaluate the performance of regression or forecasting models. It is a variant of MAPE in which the mean absolute percent errors is treated as a weighted arithmetic mean. Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume). [3]
The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean. [1]
A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean.It involves the calculation of the mean after winsorizing — replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values, [1] typically doing so for an equal amount of both ...