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where is the actual value of the quantity being forecast, is the forecast, and is the number of different times for which the variable is forecast. Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result, the formula can be used as a ...
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The use of the MAPE as a loss function for regression analysis is feasible both on a practical point of view and on a theoretical ... actual value), given by ...
In contrast to the mean absolute percentage error, SMAPE has both a lower and an upper bound. Indeed, the formula above provides a result between 0% and 200%. Indeed, the formula above provides a result between 0% and 200%.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...
Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the sample mean.
Random variations are not predictable but they do tend to follow some rules, and those rules are usually summarized by a mathematical construct called a probability density function (PDF). This function, in turn, has a few parameters that are very useful in describing the variation of the observed measurements.
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.