Questions tagged [statistics]
653 questions
7
votes
1 answer
Is there a stable numerical algorithm for FWHM that isn't 2.35*sigma?
This is a question that should have a simple answer, but which I can find no proper discussion of in the literature or on the internet.
I start from the assumption that I have a noisy numerical signal with a peak in it - for example amplitude as a…
Hywel
- 591
5
votes
2 answers
Are all discovered normal distribution in the physical world a result of central limit theorem?
Apart from the wave function in a harmonic well. Are all discovered normal distribution in the physical world a result of central limit theorem?
If it is the case, it may allow some reverse reasoning when we see another normal distribution. Though I…
somebody4
- 227
3
votes
1 answer
PDF from number of standard deviations plot
I must consider plots like these
where the bounds on $x$ (in this case $\sin^2\theta_{12}$ or $\delta/\pi$) are shown in terms of the number of standard deviations $N\sigma$ from the best-fit value.
How can I obtain the PDF of the $x$ values from…
mrf1g12
- 528
- 2
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1
vote
1 answer
Kullback information proof
In regards to the Kullback information (also here), I'm trying to prove that:
$$K[p_1,p_2] = \int dx \ p_1(x,t) \ ln\frac{p_1(x,t)}{p_2(x,t)}$$
is non-negative, whereby $p_1(x,t)$ and $p_2(x,t)$ are any two probability densities.
Therefore, I've…
B4ckflip1
- 11
1
vote
1 answer
Example for a physical distribution without a well-defined standard deviation
Is there a physical example of a distribution that has a diverging standard deviation (like the Cauchy distribution) and is there an intuitive reason for the standard deviation diverging?
Is there a physical context where I should expect my standard…
konstle
- 758
1
vote
0 answers
How do I find the uncertainty range of experimental data given this constraint on the standard deviation?
We have an inequality relating the standard deviation of position, $σ_x$, and the standard deviation of momentum, $σ_p$:
$$σ_x × σ_p ≥ \,\frac{h}{4π}$$
Where $\frac{h}{4π} = 5.27285909 × 10^{-35} \text{ J s}$.
Say we record a position value $x = 0.4…
Lawton
- 327
1
vote
0 answers
Bayesian error propagation: How to get probability of event given many outcomes and many realizations of process?
Imagine that a point is space x can be characterized by either A,B,C,D,E,F,G in the c_A, c_B .. classifications of x as A,B,C,... My data gives:
P(x = A | c_A) = f_A(x)
P(x = B | c_B) = f_B(x) and so on.
What I want to ask is what x most probably is…
Suyama87
- 43
- 5
1
vote
0 answers
Quantity with approximate lognormal distribution
I am studying a quantity $x$ for which $\log( x)$ is nearly (although not exactly) lognormal. What would be the appropriate "typical" value: the mean $\langle x\rangle$ or rather $e^{\langle\log(x)\rangle}$?
lagoa
- 311
0
votes
2 answers
Is there a fundamental difference between the statistical methods of science, comparing medicine to physics?
Is there a fundamental difference between the statistical methods of science, comparing medicine/biology with small sample sizes(n < 10^2 or 10^3) to the statistics applied in Quantum Mechanics (h: order 10^34) or statistical mechanics (N: order…
TestPilotDoc
- 43
0
votes
1 answer
Calculating basic systematic error
My lab partner and I are in disagreement about what the systematic error of our temperature measurement is.
The digital temperature gauge measured to one decimal place (i.e 20.3°C). We took a number of readings.
I think that the systematic error is …
Acrux
- 15
0
votes
1 answer
I am studying fragmentation warheads and this formula of 'numbers of fragments hitting the target' is just not making sense
What is parameter 'p' in the formula? If somebody knows any better source to study this part... welcome to suggest. Thanks a lot.
Probable Number of Fragments Hitting the Target
It can be proven that the fragments from a typical warhead are…
Ad Sinc
- 13
0
votes
1 answer
How to estimate errors of experimental values like velocity of a wave which have no theoretical values?
I managed to come up that it would be good to use normal distribution and standard deviation acquired from it since there's no value to compare with. But I have no idea how to proceed. Is there any known method which uses normal distribution?
i9100
- 407
0
votes
1 answer
Different units on y-axis
I was just wondering if you can have different units on the same y-axis? For example, if I'm graphing blood flow, oxygen level and skin temperature against time in one graph. I can put temperature on the secondary y-axis, but I would still have two…
Julia Yin
- 3
- 1
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0
votes
1 answer
The discrepancy between the two values in units of sigmas?
Assuming gaussian error distributions, how to calculate the discrepancy between the two values in units of sigmas?
Newman
- 2,566
0
votes
2 answers
More data points or more averages?
Perhaps an elementary questions. Given a time limited measurement situation, would it be better for one to measure more averages or more data points?
More averages will increase the SNR by $$\sqrt{n}$$ , i.e., making the data point more reliable,…
Dan
- 111