Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [error-propagation]

For questions on propagation of errors.

In statistics, propagation of errors or propagation of uncertainty is the effect of variables' errors or uncertainties on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the function.

388 questions
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Multiplication and division of values with geometric standard deviation

What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ? It is a frequent situation in science, that the the signal of the machines is in…
Barbara
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Avoiding loss of numerical accuracy

I need to to evaluate the function $f(x) = {1 - (1-A)^x \over A}$, where $0 < A \leq 1$ and $0 \leq x \leq 1$. A straightforward C implementation of $f(x)$ with floating-point arithmetic works fine as long as A is reasonably large, but it breaks…
Stumped
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What's best, to take the average of 2 measures or the square root of their product (in this case)?

I have a physical system where a real and positive quantity A can be measured by two ratios between 4 measures, $\frac{B}{C}$ and $\frac{D}{E}$ (all of them are positive real numbers). From the expressions I got from error propagation I'm having the…
user2934303
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Uncertainty/error calculation (product of number and trig)

I understand how to multiply two numbers with errors together. However, I am unsure how to do a problem when there is trig involved: $$ (100 \pm 10) \cdot \sin(30 \pm 1) $$ What are the steps I should take to solve it?
JavaNoob
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How to find the error of the Pythagorean Theorem equation?

I am trying to find the length of a hypotenuse with error, when the measurements of the two legs have an error. So for this equation $$C = \sqrt{A^2+B^2}$$ when $A$ and $B$ each have an error of $\sigma_A$ and $\sigma_B$ respectively.
unknownnine9
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How to divide by a number with error

How do I divide a constant number by a number with error? For example... $$\frac{1}{(101 \pm 0.0058)} = 0.0099 \space\pm\space ???$$ Please help!
mwsmws100
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Absolute and Relative Error of $x^y$

Suppose that we have two measured values $x$ and $y$ with maximum absolute errors of $e_x$ and $e_y$. Is there a formula to find a good upper bound for absolute and relative error of $x^y$?
Mohammad Javad Naderi
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Propagation of Errors with Time Derivatives

I've been searching the internet for a few weeks and picking the brains of colleagues in person without success. As to what happens to error propagating down a derivative when the error in a measurement is known. (Hopefully I'm on the right SE,…
Brandon Murray
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Where does the error propagation formula comes from?

As an engineering student I have come several times across the formula $$\sigma_{f(\vec{x})}=\sqrt{\sum_{i} \big (\dfrac{\partial f}{\partial x_{i}}\sigma_{x_{i}}\big )^{2}}$$ for the propagation of errors, but I never understood where does it come…
Francisco
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Trying to understand an inconsistency within basic error analysis equations

While doing a physics lab, I noticed that the error analysis equation for multiplication $$R = \frac{X*Y}{Z}$$ $$ \delta R = |R|\sqrt{\left(\frac{\delta X}{X}\right)^2+\left(\frac{\delta Y}{Y}\right)^2+\left(\frac{\delta Z}{Z}\right)^2}$$ is not…
Ryan
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Is this a correct error propagation implementation?

Assume $x_i$s are identical and independent random variables. I have a function $$ g= 2 - \frac{\sum_i x_i^2/N}{\left ( \sum_i x_i/N \right)^2} $$ (where $N$ is the number of $x_i$s in the sum) from which I'd like to estimate an error. I…
user110503
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Error propagation for sine function, in terms of degrees and radians

For a measurement $\theta$ with uncertainty $\Delta\theta$, the propagated error of the sine function is given by $$\Delta(\sin\theta) = (\cos\theta)\cdot\Delta\theta$$ However I note that if $\theta$ is given in terms of radians and degrees,…
Tian
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What is output noise or uncertainty (error propagation) for a min or a max function?

For an input vector X = {${x_1 , x_2, ..., x_i, ..., x_n}$} with input noise as a variance-covariance matrix. If I perform $max$(X). What is the output uncertainty or noise. Also, is the assumption that if $x_i$ is the $max$ of X, then is the output…
Sreenivas Murali
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What does it mean to calculate a number to $n$ decimals of exactness.

I was asked to numerically calculate Bessel functions for certain points and report their values to "6 decimal places of exactness". I did this in matlab and there's no truncate function, so I was forced to round the number. However this got me…
ben ari
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Uncertainty in distance from uncertainty in coordinates

I know this is basic, but I've managed to get myself confused. So, I have an object at location $(x,y,z)$ with uncertainty in the location of $(\delta x, \delta y, \delta z)$. What is the uncertainty in the distance from the origin to the object? …
bob.sacamento
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