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The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures, the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal. However, it ...
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.
the weighted arithmetic mean of the median and two quartiles. Winsorized mean an arithmetic mean in which extreme values are replaced by values closer to the median. Any of the above may be applied to each dimension of multi-dimensional data, but the results may not be invariant to rotations of the multi-dimensional space. Geometric median
A Bayesian average is a method of estimating the mean of a population using outside information, especially a pre-existing belief, [1] which is factored into the calculation. This is a central feature of Bayesian interpretation. This is useful when the available data set is small. [2] Calculating the Bayesian average uses the prior mean m and a ...
The median of a power law distribution x −a, with exponent a > 1 is 2 1/(a − 1) x min, where x min is the minimum value for which the power law holds [10] The median of an exponential distribution with rate parameter λ is the natural logarithm of 2 divided by the rate parameter: λ −1 ln 2.
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
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]
q = 0 corresponds to the weighted harmonic mean, q = 1 to the weighted geometric mean, and; q = 2 to the weighted arithmetic mean. As q approaches infinity, the weighted generalized mean with exponent q − 1 approaches the maximum p i value, which is the proportional abundance of the most abundant species in the dataset.