For questions on propagation of errors.

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1answer
9 views

Standard Error for Weighted Values

I want to calculate the standard error for an experimental measurement. The data is stored as a 2D image which is circularly symmetric about a center point. To reduce the data we radially integrate ...
4
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1answer
469 views

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 ...
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0answers
15 views

Statistical uncertainty on a percentages inferred from an A/B test

Question: What is the statistical uncertainty on percentages inferred from an A/B test? Example: $N = 100$ people are presented with an A/B choice (e.g., jumping into shark-infested water, choosing ...
3
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3answers
217 views

How to calculate the standard deviation of numbers with standard deviations?

I have essentially a propagation-of-error problem I run into frequently with my scientific data. For example, I have three samples, each of which I take two measurements of. So, for each sample, I can ...
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2answers
28 views

How can I calculate the uncertainty of two combined uncertainties?

If uncertainty can be calculated as half the range, and percentage uncertainty is the uncertainty over a mean all multiplied by 100, how can I find what the uncertainty is of A^2 * B^3 when A = 21.3 ...
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2answers
42 views

Prove that the rounding error can contaminate half the digits of computed root

I am trying to resolve the following problem: If $b^2 \approx 4ac $ the rounding error can contaminate half the digits of the root computed with the formula: $\dfrac {-b \pm \sqrt {b^2 - 4ac}} ...
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1answer
41 views

Prove graphically that the Lambert equation has exactly zero, one or two roots

I need some help on the below problem. Consider the Lambert equation: $xe^x = a$ for real values of x and a (a) Show graphically that the equation has exactly one root $ \xi(a) \ge 0 $ if $ ...
1
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1answer
21 views

How does one bound computational error for a finite difference approximation of the second derivative?

I'm trying to wrap my head around ways to minimize total computational error (defined as a sum of the bounds on the truncation and rounding errors) by taking a differentiable function $f : \mathbb{R} ...
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1answer
36 views

Statistical methods in experiments

I'm currently facing a huge problem in manipulating raw data from an experiment. Suppose I have the set of data: $$T_1=6.12 \pm 0.001s,\\ T_2=4.90875 \pm 0.001s, \\ T_3=3.9 \pm 0.001s, \\ T_4=3.69 ...
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0answers
22 views

Error of 2 correlated variables, proxied as random variables

Disclaimer: my 1st question in math.stackexchange (usually in stackoverflow !), and non-English speaker. I'm trying to solve this problem for an arbitrary no. of variables, with multiple categories ...
0
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1answer
21 views

How to show the relative error of $ \frac{x_A}{y_A}$

First, this is how the relative error of $x_Ay_A$ (approximated errors) is computed as compared to $x_Ty_T$ (true errors) - $ \displaystyle Rel(x_Ay_A) = \frac{x_Ty_T - x_Ay_A}{x_Ty_T}$, Letting ...
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0answers
17 views

Is there a standard method in finding the maximum of the following?

This is an elementary level exercise in error estimation. The figure shows that, from a rectangular plate AXBYCDZF, another smaller rectangular plate EDZF is cut off. {$AB = a, BC = b, XB = p$ and ...
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0answers
19 views

John Von Neumann Error distribution

I have a sort of general question. John Von Neumann proposed am error distribution function as following. $error = A*e^{ikx} $ with k: the wavenumber Now our professor asked us, why is it so ...
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0answers
44 views

Is the Taylor Expansion a good approximation

Say I use a computer to sum the first 26 terms of $e^{-5}$ (degree 25), will this taylor expansion provide a good approximation? It summed to $.0067$ To me this seems like a good approximation, but I ...
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0answers
20 views

Link between total diffential and error caculation?

I earlier asked this question Error propagation, why use variences?. And am now slightly confused about the link between error propagation and total diffentials. As mentioned in the linked question, ...
2
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1answer
42 views

Error propagation, why use variences?

I have been reading up on error propagation and am slightly confused about something. We can the error in $c=f(a,b)$ as the: $$\sigma(c)= f_a \sigma_a+f_b \sigma _b$$ Firstly is this correct and am I ...
2
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0answers
379 views

How to estimate variances for Kalman filter from real sensor measurements without underestimating process noise.

As the title says, I want to estimate the variances needed for a Kalman filter from real sensor measurements only. For example we can take a temperature sensor, but the solution shall be as ...
0
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1answer
26 views

Error Propagation of parameter in an irreversible equation

I have the following equation that predicts a certain parameter $c_t$: $$c_t = f(x,y_1,y_2,y_3...)$$ The function $f$ is known, continuous, real, differentiable to all arguments and the solution to a ...
2
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0answers
73 views

Accuracy of distance and bearing between GPS locations

I'm writing on an Android app that tracks the distance and bearing between two GPS location (each from a different device). Finding the mean distance and angle between the devices is quite easy, and ...
0
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2answers
26 views

Absolute error in machine-precision terms.

I am trying to wrap my head around errors in floating point calculations. Let me denote absolute error as follows: $e = |x - \hat{x}|$, where $x$ is the exact number and $\hat{x}$ is its floating ...
2
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1answer
22 views

Relative Error $\frac{x-x_0}{x}$

According to many definitions I've seen the relative error is defined by $$E = \frac{x-x_0}{x}$$ where $x$ is the "true" value. But some people use instead $$\frac{x-x_0}{x_0}. $$ Is this incorrect? ...
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3answers
407 views

Calculate uncertainty of sine function result

I have an angle given in degrees: $$\theta_{\min} = 63^{\circ} \pm 0.5^{\circ}$$ I need to calculate it's sine and still know the uncertainty of the value: $$n = 2\sin(\theta_{\min}) = ...
0
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1answer
93 views

Stopwatch Accuracy and Precision

Let's say I have a stopwatch that can take split times. It's resolution is 1/100th of a second. Let's also say I have a robot that can press the split button exactly 0.244s apart in real time. I have ...
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0answers
33 views

Accounting for drop-outs in clinical trials

'Physical Therapy Review' [Intention to treat analysis, compliance, drop-outs and how to deal with missing data in clinical research: a review Susan Armijo-Olivo, Sharon Warren and David Magee Faculty ...
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0answers
68 views

Expand $\int_{-1}^0 e^{a\cos{\theta}}J_0(b\sin{\theta})\,d\cos{\theta}$ in spherical harmonics.

I want to solve the integral (a probability density function) $$ g(\gamma)=\int_{-1}^0 e^{-f\cos{\theta}\cos{\gamma}}J_0(-if\sin{\theta}\sin{\gamma})\,d\cos{\theta} $$ numerically, everything is ...
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0answers
14 views

Error propagation of non-square Matrix

I measure values of the vector $\vec{P}$ where each value $P_i$ has its own error $E_i$. I'm interested in the vector $\vec{K}$. Both values are linked by $\vec{K} = M \vec{P}$ . Since $\vec{P}$ and ...
2
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0answers
52 views

Show that $\displaystyle\sum_{i=0}^{N-1}|\epsilon_i|\to0, N\to\infty$

Let $I_o=[t_0,t_0+T]\subset\mathbb R, T>0$, If $f\in C^0(I_0\times\mathbb R,\mathbb R)$ and satisfies the Lipschitz condition: $\forall t\in I_0, \forall y,y^{*}\in\mathbb ...
0
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1answer
121 views

Relative error % of cos and sin functions?

I've been searching all over the net and I can't seem to find a definitive answer - perhaps I'm asking the wrong question. How does one calculate the relative error (%) of the cos/sin/tan of an angle ...
0
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1answer
45 views

Sum of positive integers estimating sum of fractions

Given $m$ fractions adding up to an positive integer $n$ For example: $m=3\\n=10=\frac{30}{6}+\frac{20}{6}+\frac{10}{6}$ How can we find $m$ positive integers that sum to $n$ (a partition of $n$), ...
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1answer
26 views

Statistics on discrete probability with error?

I need help with this question, am pretty confused on what to do with the error, I can't see how to use it.
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0answers
25 views

Looking for a motivating example for backward error analysis

For many people, it seems self-evident that backward error is a powerful tool in numerical analysis. But for me, it is hard to imagine a situation in which backward error analysis provides any useful ...
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0answers
41 views

Error propagation in pearson correlation

I have two data-sets $X$ and $Y$ with errors $\Delta X$ and $\Delta Y$. I calculated the Pearson Sample Correlation $r$. Is it possible to calculate the error of $r$ using propagation of uncertainty: ...
1
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1answer
260 views

Error Estimation and Propagation through Trigonometric Functions

I have a problem whereby I have to estimate the absolute error of a value calculated using values read from sensors. The equation used to calculate the value is $T_{xy} = R \tan \theta$. The sensor ...
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2answers
43 views

Order of error of a fraction

If two functions can be written as the sum of some expression and an error term of higher orders of error $\epsilon$: $$f(x+\epsilon)=f_0(x,\epsilon)+O(\epsilon^m)\quad \text{ and} \quad ...
3
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2answers
115 views

Regression with error coming from rounding

I am looking at the following model: $c$ is a fixed vector in $\mathbb{R}_+^n$ and for any $x \in \mathbb{R}_+^n$ we obtain a value $y =[c^Tx]$, i.e. rounding $c^Tx$ to the nearest integer. I want ...
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1answer
609 views

What is the error in calculated volume of cylinder, given the measurements of length and radius?

Measured length of the rod is $15 \pm 0.4$ cm and the radius of the rod is $6.1 \pm 0.2$ cm. What is the error in calculated volume? (two decimal places) What i've tried is $$V=\pi r^2 l$$ ...
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1answer
337 views

How to calculate uncertainties?

A question requires me to make a calculation involving variables with uncertainties, giving my answer with its result uncertainty. How do I do that?
0
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1answer
162 views

Drove 238 miles and used 27.3 litres of petrol: find upper bound for consumption per mile, considering measurement errors

X drove 238 miles, correct nearest mile. They used 27.3 litres of petrol, to the nearest tenth of a litre. $Petrol Consumption =$${Miles}\over Petrol Used$ Work out the upper bound. I used ...
1
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1answer
51 views

Uncertainty in measurements: if $x$ has uncertainty $\pm\epsilon$, what is the uncertainty in $\sin x$?

I have two questions regarding uncertainties in measurements. First, if I have some measured value for $x$ with an uncertainty $\pm e$, what would be the uncertainty in $\sin x$, $\pm\sin e$? ...
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0answers
21 views

How to find error constant, global and local error of ODE integration method

In literature regarding open channel flows I bumped into strange ODE integration methods: the first one: $$y_{i+1}=y_i+\Delta x\cdot\sqrt{f_i\cdot f_{i+1}}$$ the second one $$y_{i+1}=y_i+\Delta ...
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0answers
43 views

Propagation of variance/covariance for $L_1$ Estimator with no analytic solution

This is my first question on Math Exchange so my apologies if it does not initially fit the format. I have a problem where I'd like to calculate the a-posteriori variance/covariance matrix of ...
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0answers
52 views

what are some good ways to define the errors between two functions?

I have two functions. One is the original function (that contains 4 variables), and the second one is the approximation to the first one (also contains 4 variables). The question is, if I want to ...
0
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1answer
21 views

What is the error on a counting variable?

I don't know if a variable that acts as a counter has an associated error. I don't see it as a measured quantity so I think that it has no error. The problem is this: you have an image of a star and ...
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0answers
8 views

To find error in time histogram

I have a data which is recorded from a detector. Whenever the detector produce signal it records the time. I have recorded the data for several cycles, one cycle is 0 to 1 second. Finally I made the ...
2
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1answer
128 views

Margin of error for quotient of two measurements

I need to find the total margin of error for calculating velocity, while I have margins of error for time and distance. Actually the margins are the same (as both measurements were based on GPS - but ...
1
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1answer
46 views

Help in Measuring Error on Estimates of Differential Equations

I am working on a project for class where I have to estimate the solutions to a damped harmonic oscillator ($x''+2 \gamma x'+ \omega^2 x=0$) and compare three methods for doing so (Third Order ...
2
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0answers
39 views

Monte Carlo with error on individual samples

I'm performing a Monte Carlo integration where the individual samples have an error, and I'm wondering how to estimate the final error. Some more detail: The integral E I'm after is estimated in the ...
0
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1answer
30 views

Error propagation for ratio data

I'm working with some published ratio data for isotopes of uranium (238U) and lead (208Pb and 206Pb). The data are published in ratios of 238U/208Pb and 206Pb/208Pb, but I need the data to be in the ...
2
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0answers
38 views

Yacov Perelman Nepero game

This is my first question, so sorry if I'll make any mistake in using the site formatting. I found this game on a book by Yacov Perelman and I thought it could be nice to introduce Nepero number to ...
0
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1answer
52 views

Mean of data with uncertainties and confidence interval

My question sounds rather simple, but sadly I have not been able to find an answer online (which is rather strange as this seems very basic, so I apologize if I simply haven't looked well enough) The ...