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Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
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% ...
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 ...
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g.
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 ...
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 ...
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.
Jacobus van 't Hoff (1852–1911), an influential theoretical chemist and the first winner of the Nobel Prize in Chemistry.. Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular ...