For questions on propagation of errors.

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Uncertainty of Multiplication using Absolute Uncertainties

I am about to calculate the uncertainty of a measurement device. The formula of the result can be written as $$P=\frac{V}{R \times G}$$ All three values are uncertain; for $R$ and $G$, both the ...
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6 views

Error propagation with repeated values in the numerator and detonator

How would you do error propagation on an equation like this: $C=\left(\frac{A-B}{A B}\right)$ where A has error ฯƒa and B has error ฯƒb I would guess you use standard text book relations but since A ...
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1answer
12 views

How to estimate the error on the position of the point x where y is maximal in quadratic relationships?

I would like to estimate the elevation at which species richness is expected to be maximal. The relationships between species richness ($y$) and elevation ($x$) follows a second order polynomial ...
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9 views

Error propagation for multiparameter-non-linear fit with covariance matrix.

I have created a multiparameter-fitted-function for some data: $๐’‡(๐’™)=๐‘จ๐’™^{(๐‘ช+๐Ÿ)}๐’†^{โˆ’(\dfrac{(๐‘ช+๐Ÿ)๐’™}{๐‘ฉ})}+๐‘ฌ๐’™^{(๐‘ฎ+๐Ÿ)} ๐’†^{โˆ’(\dfrac{(๐‘ฎ+๐Ÿ)๐’™}{๐‘ญ})}$ I know the values and absolute ...
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27 views

If $\theta = (59.3\pm 1.2)^{\circ} $, find $\tan(\theta)$ and it´s uncertainty.

How can I find the uncertainty? I need to use this formula: The general formula for uncertanties is: $\sigma_q = \sigma_q (a,b,c,...)$ and $\mathrm{Cov}(a,b,c,...)=0$ $\,\,$then $$\sigma_q ^2 = ...
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1answer
34 views

How to propagate uncertainties in the dependent variable when doing linear regression?

Let's say I have an independent variable $\vec x$ and a dependent variable $\vec y$ and measurement errors on my dependent variable that I know to be $\delta y$. For the sake of simplicity, let's say ...
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14 views

What is the source of the error in the Sherman-Morrison formula application?

The Sherman-Morrison formula results in small errors in relation to the standard matrix inverse operation after each application, as shown here. From what I understand, the Sherman-Morrison identity ...
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1answer
17 views

About absolute error calculation

Given a prism immersed in the air with an opening angle equal to $\alpha = \bar{\alpha} \pm \Delta\alpha = 60ยฐ \pm 1ยฐ$ and $\delta = \bar{\delta} \pm \Delta\delta = 45ยฐ \pm 2ยฐ$ is the angle of minimum ...
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15 views

To what set do measured values belong?

This question is more conceptual than practical. It seems that when we apply mathematics to measured values, we treat them like real numbers. When measured values take error into account using ยฑ ...
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15 views

Measure of how well a 3D function represents experimental data

I have experimental data of a one dimensional heat equation and corresponding values for a predicted temperatures. Is there any method in which I could statistically analyse the data to determine if ...
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17 views

Error propagation with dependent errors

I have a function $f(x_1,\ldots,x_n)$ where the variables $x_k$ have errors $\delta_k$. If these errors are independent I can add them root mean square: $\delta ...
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1answer
22 views

round-off error of sample

Basic question: If I have a large set of numbers where the third decimal has been rounded off. For example $a_1 = 5055.29$ $a_2 = 1755.13$ $a_3 = 1083.03$ $a_4 = 335.99$ $(...)$ If I sum all ...
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11 views

low number poissonian errors: is it possible for a measurement of 4 counts to have a significance higher than 2 sigma?

What is the best way to measure statistical significance of an overdensity in counting experiment where you have small numbers? Rather than bore you with my actual problem, please consider the ...
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12 views

Error on determinant from statistical errors on complex matrix elements

Say I have a complex matrix $A$ whose elements $A_{ij}$ have statistical error $\delta_{ij}$. I need to figure out from these errors what will be the error on the determinant $|A|$. If the matrix was ...
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29 views

Calculating absolute error. Teacher distributes the abs value signs.

Ill illustrate my confusion with an example: It can be shown, assuming $E_xE_y=0$ that the error in an arithmetical multiplication will be: $E_{xy}=xE_y+yE_x+\mu$ Where $\mu$ is the so called ...
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8 views

Propagating uncertainties in Gaussian fit

I'm doing an analysis where I have a set of random variables with some known uncertainties (the uncertainties are different for each random variable). The random variable is roughly Gaussian ...
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21 views

Geometric Mean of Random Variables

I measure a series of $n$ objects [O_1, O_2, O_3, ..., O_n]. Because those measurements are quite hard to perform, I have quite a lot of measurement error and ...
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21 views

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 ...
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1answer
16 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 ...
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20 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 ...
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2answers
35 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
43 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
42 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 $ ...
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1answer
28 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
38 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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27 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 ...
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1answer
23 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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23 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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21 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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46 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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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, ...
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1answer
51 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 ...
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1answer
882 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 ...
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1answer
32 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 ...
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94 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 ...
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2answers
30 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 ...
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1answer
25 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
681 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}) = ...
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1answer
114 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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38 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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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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15 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 ...
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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 ...
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1answer
175 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 ...
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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
27 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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3answers
406 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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28 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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52 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: ...
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2answers
48 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 ...