Absolute Error Formula Wikipedia
Contents |
close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by M A E = 1 n ∑ i = 1 n | f i −
Absolute Error Formula Chemistry
y i | = 1 n ∑ i = 1 n | e i absolute error formula physics | . {\displaystyle \mathrm {MAE} ={\frac {1}{n}}\sum _{i=1}^{n}\left|f_{i}-y_{i}\right|={\frac {1}{n}}\sum _{i=1}^{n}\left|e_{i}\right|.} As the name suggests, the mean absolute error is an
Mean Absolute Error Formula
average of the absolute errors | e i | = | f i − y i | {\displaystyle |e_{i}|=|f_{i}-y_{i}|} , where f i {\displaystyle f_{i}} is the prediction and y i {\displaystyle y_{i}} the absolute error formula excel true value. Note that alternative formulations may include relative frequencies as weight factors. The mean absolute error is on same scale of data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between series on different scales.[1] The mean absolute error is a common measure of forecast error in time [2]series analysis, where the terms "mean absolute deviation" is maximum absolute error formula sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally. Related measures[edit] The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the mean absolute scaled error (MASE) and the mean squared error. These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the mean signed difference. Where a prediction model is to be fitted using a selected performance measure, in the sense that the least squares approach is related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2011) (Learn how and when to remove this template message) This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2011) (Learn how and when to remove this template message) See also[edit] Least absolute deviations Mean absolute pe
may be challenged and removed. (December 2009) (Learn how and when to remove this template message) The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a
Absolute Error Formula Maths
measure of prediction accuracy of a forecasting method in statistics, for example in absolute error and relative error formula trend estimation. It usually expresses accuracy as a percentage, and is defined by the formula: M = 100 n
Absolute Deviation Formula
∑ t = 1 n | A t − F t A t | , {\displaystyle {\mbox{M}}={\frac {100}{n}}\sum _{t=1}^{n}\left|{\frac {A_{t}-F_{t}}{A_{t}}}\right|,} where At is the actual value and Ft is the forecast value. https://en.wikipedia.org/wiki/Mean_absolute_error The difference between At and Ft is divided by the Actual value At again. The absolute value in this calculation is summed for every forecasted point in time and divided by the number of fitted pointsn. Multiplying by 100 makes it a percentage error. Although the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application [1] It cannot be https://en.wikipedia.org/wiki/Mean_absolute_percentage_error used if there are zero values (which sometimes happens for example in demand data) because there would be a division by zero. For forecasts which are too low the percentage error cannot exceed 100%, but for forecasts which are too high there is no upper limit to the percentage error. When MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low. This little-known but serious issue can be overcome by using an accuracy measure based on the ratio of the predicted to actual value (called the Accuracy Ratio), this approach leads to superior statistical properties and leads to predictions which can be interpreted in terms of the geometric mean.[1] Contents 1 Alternative MAPE definitions 2 Issues 3 See also 4 External links 5 References Alternative MAPE definitions[edit] Problems can occur when calculating the MAPE value with a series of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error, caused by a small deviation in error, can occur. As an
the quantity being forecast. The formula for the mean percentage error is MPE = 100 % n ∑ t = 1 n a https://en.wikipedia.org/wiki/Mean_percentage_error t − f t a t {\displaystyle {\text{MPE}}={\frac {100\%}{n}}\sum _{t=1}^{n}{\frac {a_{t}-f_{t}}{a_{t}}}} where https://en.wikipedia.org/wiki/Mean_squared_error at is the actual value of the quantity being forecast, ft 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 absolute error errors can offset each other; as a result the formula can be used as a measure of the bias in the forecasts. A disadvantage of this measure is that it is undefined whenever a single actual value is zero. See also[edit] Percentage error Mean absolute percentage error Mean squared error Mean squared prediction error Minimum mean-square error Squared deviations absolute error formula Peak signal-to-noise ratio Root mean square deviation Errors and residuals in statistics References[edit] Khan, Aman U.; Hildreth, W. Bartley (2003). Case studies in public budgeting and financial management. New York, N.Y: Marcel Dekker. ISBN0-8247-0888-1. Waller, Derek J. (2003). Operations Management: A Supply Chain Approach. Cengage Learning Business Press. ISBN1-86152-803-5. Retrieved from "https://en.wikipedia.org/w/index.php?title=Mean_percentage_error&oldid=723517980" Categories: Summary statistics Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main pageContentsFeatured contentCurrent eventsRandom articleDonate to WikipediaWikipedia store Interaction HelpAbout WikipediaCommunity portalRecent changesContact page Tools What links hereRelated changesUpload fileSpecial pagesPermanent linkPage informationWikidata itemCite this page Print/export Create a bookDownload as PDFPrintable version Languages Add links This page was last modified on 3 June 2016, at 14:20. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view
deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors or deviations—that is, the difference between the estimator and what is estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or quadratic loss. The difference occurs because of randomness or because the estimator doesn't account for information that could produce a more accurate estimate.[1] The MSE is a measure of the quality of an estimator—it is always non-negative, and values closer to zero are better. The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and its bias. For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard deviation. Contents 1 Definition and basic properties 1.1 Predictor 1.2 Estimator 1.2.1 Proof of variance and bias relationship 2 Regression 3 Examples 3.1 Mean 3.2 Variance 3.3 Gaussian distribution 4 Interpretation 5 Applications 6 Loss function 6.1 Criticism 7 See also 8 Notes 9 References Definition and basic properties[edit] The MSE assesses the quality of an estimator (i.e., a mathematical function mapping a sample of data to a parameter of the population from which the data is sampled) or a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable). Definition of an MSE differs according to whether one is describing an estimator or a predictor. Predictor[edit] If Y ^ {\displaystyle {\hat Saved in parser cache with key enwiki:pcache:idhash:201816-0!*!0!!en!*!*!math=5 and timestamp 20160929113630 and revision id 741744824 8}} is a vector of n