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Kernel average smoother example. 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 to X 0 (the closer to X 0 points get higher weights).
The method can easily be extended to other dimensional spaces and it is in fact a generalization of Lagrange approximation into a multidimensional spaces. A modified version of the algorithm designed for trivariate interpolation was developed by Robert J. Renka [4] and is available in Netlib as algorithm 661 in the TOMS Library.
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.
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 ().
The expected value of a random variable is the weighted average of the possible values it might take on, with the weights being the respective probabilities. More generally, the expected value of a function of a random variable is the probability-weighted average of the values the function takes on for each possible value of the random variable.
[2] [3] The PERT distribution is widely used in risk analysis [4] to represent the uncertainty of the value of some quantity where one is relying on subjective estimates, because the three parameters defining the distribution are intuitive to the estimator. The PERT distribution is featured in most simulation software tools.
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 ...
EWMA weights samples in geometrically decreasing order so that the most recent samples are weighted most highly while the most distant samples contribute very little. [ 2 ] : 406 Although the normal distribution is the basis of the EWMA chart, the chart is also relatively robust in the face of non-normally distributed quality characteristics.