Updating mean and variance estimates an improved method
can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Thus this algorithm should not be used in practice.
For samples containing many values very close to the mean, this function is subject to inaccuracy due to catastrophic central moments of a sample.
For samples containing many values very close to the mean, this function is subject to inaccuracy due to catastrophic cancellation. This function performs two passes over the sample, so is not subject to stream fusion.
(It is not the only alternative, for a detailed numerical study of possible options, see the paper linked below.) The West algorithm supports mean and variance computation for positively weighted samples Alternative algorithms and variants for higher-order moments can be found on the excellent Wikipedia page on the topic.
For unweighted variance $$\text(X):=\frac\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: $$\text(X):=\frac\sum_i(x_i - E[X])^2$$ I'm looking into weighted mean and variance, and wondering what the appropriate bias correction for the weighted variance is.
Other applications are discussed as well including the use of updating formulae in a parallel computing environment.
we present resume and rounding error analyze son several numerical schemes.
In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the optimality of an estimator, of an experimental design or of an hypothesis testing procedure.
Essentially, a more efficient estimator, experiment or test needs fewer samples than a less efficient one to achieve a given performance.
Giving or procuring evidence is the process of using those things that are either (a) presumed to be true, or (b) were themselves proven via evidence, to demonstrate an assertion's truth.