In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.
The formula for the mean percentage error is:
:
where ''a''
''t'' is the actual value of the quantity being forecast, ''f''
''t'' is the forecast, and ''n'' 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 measure of the
bias
Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, ...
in the forecasts.
A disadvantage of this measure is that it is undefined whenever a single actual value is zero.
See also
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Percentage error
The approximation error in a data value is the discrepancy between an exact value and some '' approximation'' to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute e ...
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Mean absolute percentage error
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula:
: ...
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Mean squared error
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between ...
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Mean squared prediction error
In statistics the mean squared prediction error or mean squared error of the predictions of a smoothing or curve fitting procedure is the expected value of the squared difference between the fitted values implied by the predictive function \wid ...
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Minimum mean-square error
In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In ...
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Squared deviations
Squared deviations from the mean (SDM) result from squaring deviations. In probability theory and statistics, the definition of ''variance'' is either the expected value of the SDM (when considering a theoretical distribution) or its average valu ...
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Peak signal-to-noise ratio
Peak signal-to-noise ratio (PSNR) is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic ...
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Root mean square deviation
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents ...
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Errors and residuals in statistics
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The err ...
References
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* {{cite book , year=2003 , author=Waller, Derek J. , title=Operations Management: A Supply Chain Approach , publisher=Cengage Learning Business Press , isbn=1-86152-803-5
Summary statistics