Percent Error When True Value Is 0
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Percent Error = 0
Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related percent error when actual value is zero fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How to calculate relative
Relative Error When True Value Is Zero
error when true value is zero? up vote 10 down vote favorite 3 How do I calculate relative error when the true value is zero? Say I have $x_{true} = 0$ and $x_{test}$. If I define relative error as: $\text{relative error} = \frac{x_{true}-x_{test}}{x_{true}}$ Then the relative error is always undefined. If instead I use the definition: $\text{relative error} = \frac{x_{true}-x_{test}}{x_{test}}$ Then the relative error is always 100%. Both methods seem useless. Is there another alternative? percent error when expected value is zero statistics share|cite|improve this question asked Feb 15 '14 at 22:41 okj 9511818 1 you need a maximum for that.. –Seyhmus Güngören Feb 15 '14 at 23:06 1 Simple and interesting question, indeed. Could you tell in which context you face this situation ? Depending on your answer, there are possible alternatives. –Claude Leibovici Feb 16 '14 at 6:24 1 @ClaudeLeibovici: I am doing a parameter estimation problem. I know the true parameter value ($x_{true}$), and I have simulation data from which I infer an estimate of the parameter ($x_{test}$). I want to quantify the error, and it seems that for my particular case relative error is more meaningful than absolute error. –okj Feb 17 '14 at 14:05 1 What about $\text{error} = 2 \frac{x_{true}-x_{test}}{x_{true}+x_{test}}$ if it is for an a posteriori analysis ? –Claude Leibovici Feb 17 '14 at 14:16 1 @okj. I am familiar with this situation. Either use the classical relative error and return $NaN$ if $x_{true}=0$ either adopt this small thing. It is always the same problem with that. You also can add a translation to the $x$'s to get rid of this. –Claude Leibovici Feb 17 '14 at 15:40 | show 4 more comments 4 Answers 4 active oldest votes up vote 5 down vote accepted First of all, let me precise that I am
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How To Calculate Relative Error When True Value Is Zero?
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Can Percent Error Be Zero
Products International Argentina Australia Brazil Canada France Germany India Indonesia Italy Malaysia Mexico New Zealand Philippines Quebec Singapore Taiwan Hong the absolute error divided by the true value and multiplied by 100 Kong Spain Thailand UK & Ireland Vietnam Espanol About About Answers Community Guidelines Leaderboard Knowledge Partners Points & Levels Blog Safety Tips Science & Mathematics Mathematics Next Percent error when the true value is http://math.stackexchange.com/questions/677852/how-to-calculate-relative-error-when-true-value-is-zero 0? The formula for calculating percent error is (estimated value - true value) / true value * 100. My estimated value is 0.1 while the true value is 0, which would give me (0.1 - 0) / 0 * 100. Since dividing by 0 is impossible, how can i find the percent error? Thank you!! 1 following 4 answers 4 Report Abuse Are you sure you want https://answers.yahoo.com/question/index?qid=20091020201824AAD8K12 to delete this answer? Yes No Sorry, something has gone wrong. Trending Now Philip Rivers Billy Bush Gabrielle Union Diane Kruger Shania Twain 2016 Crossovers Truman Capote Auto Insurance Quotes Samsung Galaxy Dating Sites Answers Relevance Rating Newest Oldest Best Answer: There isn't one in this case. Percent error is undefined when the denominator is zero. It's just a case where the concept of percent error isn't useful. Source(s): elifino · 7 years ago 0 Thumbs up 1 Thumbs down Comment Add a comment Submit · just now Asker's rating Report Abuse Certainly you end up dividing by zero, you cannot calculate percent error when the true value is zero. I think the idea is that you should have any error when measuring a quantity of zero. It's hard to make a measurement mistake if you have zero of the unit! To be honest, I had never considered this before, so thank you! Tim · 7 years ago 0 Thumbs up 0 Thumbs down Comment Add a comment Submit · just now Report Abuse it is normally going to be a low percent error under those circumstances. Normally the methods of measurement are in the text book. 3012345678 · 7 y
1 ( x ) = 1 + x {\displaystyle P_{1}(x)=1+x} (red) at a = 0. The approximation error is the gap between the https://en.wikipedia.org/wiki/Approximation_error curves, and it increases for x values further from 0. The approximation error in some data is the discrepancy between an exact value and some approximation to it. An https://de.mathworks.com/matlabcentral/newsreader/view_thread/306851 approximation error can occur because the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5cm but since percent error the ruler does not use decimals, you round it to 5cm.) or approximations are used instead of the real data (e.g., 3.14 instead of π). In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm. Contents 1 Formal Definition 1.1 Generalizations 2 Examples 3 Uses value is zero of relative error 4 Instruments 5 See also 6 References 7 External links Formal Definition[edit] One commonly distinguishes between the relative error and the absolute error. Given some value v and its approximation vapprox, the absolute error is ϵ = | v − v approx | , {\displaystyle \epsilon =|v-v_{\text{approx}}|\ ,} where the vertical bars denote the absolute value. If v ≠ 0 , {\displaystyle v\neq 0,} the relative error is η = ϵ | v | = | v − v approx v | = | 1 − v approx v | , {\displaystyle \eta ={\frac {\epsilon }{|v|}}=\left|{\frac {v-v_{\text{approx}}}{v}}\right|=\left|1-{\frac {v_{\text{approx}}}{v}}\right|,} and the percent error is δ = 100 % × η = 100 % × ϵ | v | = 100 % × | v − v approx v | . {\displaystyle \delta =100\%\times \eta =100\%\times {\frac {\epsilon }{|v|}}=100\%\times \left|{\frac {v-v_{\text{approx}}}{v}}\right|.} In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. Th