In
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, 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
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 measure of the
bias
Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is inaccurate, closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individ ...
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 given data value represents the significant discrepancy that arises when an exact, true value is compared against some approximation derived for it. This inherent error in approximation can be quantified and expres ...
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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 betwee ...
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Mean squared prediction error
In statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression (statistics), regression procedure is the expected value of the Square (algebra), squared pred ...
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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
A square is a regular quadrilateral with four equal sides and four right angles.
Square or Squares may also refer to:
Mathematics and science
*Square (algebra), multiplying a number or expression by itself
*Square (cipher), a cryptographic block ...
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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 either one of two closely related and frequently used measures of the differences between true or predicted values on the one hand and observed values or an estimator on th ...
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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 erro ...
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