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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 ().
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average.
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median.It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.
An exponential moving average (EMA), also known as an exponentially weighted moving average (EWMA), [5] is a first-order infinite impulse response filter that applies weighting factors which decrease exponentially. The weighting for each older datum decreases exponentially, never reaching zero. This formulation is according to Hunter (1986). [6]
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.
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.
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 ...
On the other hand, if I p is an integer then any number from the data value at that index to the data value of the next index can be taken as the quantile, and it is conventional (though arbitrary) to take the average of those two values (see Estimating quantiles from a sample).