# Tagged Questions

For questions on propagation of errors.

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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 ...
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### What should be the expected error of a 4th order Runge-Kutta integration in a multivariable (non-linear) context?

I am writing a program where the user input $n$ variables, their initial values and differential equations. They may be non-linear. To find the value of the variables at a time $(t_0 + T)$, I use 4th ...
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### Error propagation - implicit functions

I have a little problem that I should solve quickly and I'm a little bit on pressure, so that any help/tip would be of great help. I have two nonlinear equations with two unknown variables x and y ...
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### Significance and Poisson processes

Must I include the Poisson error on a new observation when considering whether it is consistent with a distribution? For example, the number of rain drops that fall into a cup per minute are recorded....
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### 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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### Minimum error in floating point approximation of an elementary function.

I need a confirmation of a thing that probably is silly. Let $x$ a floating point number representable using $e$ bits for exponent and $m$ bits for mantissa, let $f$ a be an elementary function, you ...
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### How to make a covariance matrix from multiple observations of different objects?

I have $N$ objects. From each object, I sample $M$ values $(x,y)$ like so: ...
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### Calculating a three sigma limit on data

So I have a list of data points each with their own error (eg. 3 +/- 0.2 units) and I want to determine which of the data points are within 3 sigma. To do this do I just calculate the standard ...
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### Input Error estimation

I was wondering what are the methods used to detect the input's error when having the output's error of a model. I thoroughly searched on google, but I failed to find a well explined method, or ...
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### Show that the ratio between two numbers is always proportional to the the maximum percentage error of their average?

The question is this: if we have a set of any random consecutive numbers, for example {1, 1.2, 4.2, 4.8, 5.6, 7.4, 9.8} then how can we prove that calculating the ratio between each of the numbers and ...
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### Find the absolute and relative error for a calculator with incorrect rounding

A calculator is out of order. The calculator will round up every single number to the nearest integer if the value at the first decimal digit is 6 and above, or else it rounds down the number to be ...
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### Error Propagation - functions of the mean.

Given a number of measurements $\{x_i\}$ with values distributed according to a (known) probability distribution $\rho(x)$ with a theoretical mean $\langle x\rangle = \int dx x\rho(x) = f(y)$ and a ...
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### Propagation of Uncertainties [closed]

I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, ...