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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 following example illustrates this by applying the second SMAPE formula: Over-forecasting: A t = 100 and F t = 110 give SMAPE = 4.76% Under-forecasting: A t = 100 and F t = 90 give SMAPE = 5.26%.
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 ...
The form of Eq(12) is usually the goal of a sensitivity analysis, since it is general, i.e., not tied to a specific set of parameter values, as was the case for the direct-calculation method of Eq(3) or (4), and it is clear basically by inspection which parameters have the most effect should they have systematic errors. For example, if the ...
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.
For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters.
Consider the problem of calculating the shape of an unknown curve which starts at a given point and satisfies a given differential equation. Here, a differential equation can be thought of as a formula by which the slope of the tangent line to the curve can be computed at any point on the curve, once the position of that point has been calculated.