Percent Error With Zero In Denominator
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related 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 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? 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
one value is zero(0)? For example: percentage of error when Actual Value is 0 and Recorded Value is .1 Topics Applied Mathematics × 1,096 Questions 119,265 Followers Follow Calculations × 1,873 Questions 240 Followers Follow Percentages × Topic pending review Follow Mathematics × 1,790 Questions 45,785 Followers Follow Mar 7, 2014 Share Facebook Twitter LinkedIn Google+ 0 / 1 All Answers (8) R. C. Mittal · Indian Institute of Technology Roorkee This is not necessary that one should find relative and % error http://math.stackexchange.com/questions/677852/how-to-calculate-relative-error-when-true-value-is-zero for very small values. They are important when your actual(exact) value is very large. Mar 7, 2014 Geen Paul V · Tata Consultancy Services Limited Sir, I am working on Finite Element Analysis for an aerospace company in USA. The Company Spoke wants to get ma computed values sometimes validated by hand calculation. And sometimes the actual stress value may https://www.researchgate.net/post/How_to_calculate_percentage_error_when_one_value_is_zero02 be zero. but the numerical analysis value varies by less than 1. And I was wondering how to make it in percentage. ! Mar 7, 2014 Hanno Krieger · retired from Justus-Liebig-Universität Gießen I try to follow. If you get experimental results which allow a statistical analysis (gauss or poisson distributions) you use the established methods of error calculation. If you have only a small number of results it´s without any sense to calculate average values or medians etc. So if you spent a little bit more information (possibly with an example) I could find a tip. Mar 7, 2014 Hanno Krieger · retired from Justus-Liebig-Universität Gießen Like to add a remark. You can calculate errors not before you define a reference value. Thats what I´m missing most in your question. Mar 7, 2014 Joseph Dubrovkin · Western Galilee College You can calculate lim(deltaX/X) when X->0 using l'Hôpital's rule or graphically. The relative error is important when X->0. E.g., detection limit. Mar 8, 2014 Luca Dimiccoli · Vrije Universiteit Brussel Notice that deltaX does not satisfy all th
1 ( x ) = 1 + x {\displaystyle P_{1}(x)=1+x} (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from https://en.wikipedia.org/wiki/Approximation_error 0. The approximation error in some data is the discrepancy between an exact value and some approximation to it. An 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 the ruler does not use decimals, you round it to 5cm.) or approximations are used instead of the percent error 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 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 percent error with 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. The percent error is the relative error expressed in terms of per 100. Generalizations[edit] These definitions can be extended to the case when v {\displaystyle v} and v approx {\displaystyle v_{\text{approx}}} are n-dimensional vectors, by replacing the absolute value with an n-norm.[1] Examples[edit] As an example, if the exact value is 50 and the ap