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Example of bilinear interpolation on the unit square with the z values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation.
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.
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.
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).
As most definitions of color difference are distances within a color space, the standard means of determining distances is the Euclidean distance.If one presently has an RGB (red, green, blue) tuple and wishes to find the color difference, computationally one of the easiest is to consider R, G, B linear dimensions defining the color space.
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 ().
In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.
Moving average: A calculation to analyze data points by creating a series of averages of different subsets of the full data set. a smoothing technique used to make the long term trends of a time series clearer. [3] the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series