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Both the "compatibility" function STDEVP and the "consistency" function STDEV.P in Excel 2010 return the 0.5 population standard deviation for the given set of values. However, numerical inaccuracy still can be shown using this example by extending the existing figure to include 10 15 , whereupon the erroneous standard deviation found by Excel ...
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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 ...
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The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).