[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 384

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Prival:


you have selected 100 numbers from a database, if the database is numbered from 1 to .... X in order, then maybe *2 of those 100 numbers will be X

The function rnd(2000) gerificates a random number from 1 to 2000. We took 100 values i=0...100 and calculated everything with them. Of course, the result will not be exact, because this statistic is a confidence interval - it can also be calculated and the required sample size can be determined, depending on the required accuracy

Thank you very much for your help!
 

We make a scotch tape like this

View from the other side.

Take out the string without cutting or tearing it. You can give it to the baby for the evening and it will keep him busy for sure.

 
ivandurak:

Pull out the string without cutting or tearing anything. You can slip it to the baby for the evening and it will keep him occupied for sure.

My baby did it in three minutes (5 years old:))))).
 
Mathemat:

Size is, I take it, the spread of the extremes, or what? In this case, with a known distribution, the problem can be solved.


Alexey, I know the distribution of the series. I want to know the range of extreme values. That's what you said. How ?
 
Well, let's say that if the distribution is normal, then theoretically its "range" is infinite. Practically, if you set a sufficiently small probability that a value will fall outside these values - say, 0.001 - then the spread is on the order of three sigmas from the m.o. distribution (this is calculated using the inverse of the integral Gaussian function).
 

It's about the Hearst figure. It refers to the spread, which of course is not infinite. This suggests that the spread is not determined by the area of definition of the density function, but somehow statistically. Do you know how? Or can you guess ? With me, except for the average modulus of deviation of a point from the equilibrium position (starting point) or RMS, nothing else comes to mind.

At Peters it is the Max-Min of the series. But the series is finite. I.e. we are talking about a sample of length N. Then the spread R is related to this length N by the Hurst exponent.

In Einstein for Brownian motion it is the path travelled by a Brownian particle. But it is not the length of the broken trajectory, but the distance from the starting point. But he is talking about flat or 3-dimensional motion, I need the elementary one-dimensional case. Yes, yes, exactly, price movement. :-)

Feder has all sorts of theorems about reaching time, return time, screens, etc. But the consideration there is on a different plane. I have not studied it deeply.

In general, I need a clear definition of the concept of spread to be able to calculate it having PDF. And because the price moves simply (a homogeneous tick-flow model) and discretely, and PDF of its movement at any finite number of ticks N has a finite area of definition [-N,N].

Anyway, Nikolai decided to make fun of me. He washed his hands of the question and moved the arrows to this thread. And here it turns out to be such a relevant and up-to-date statement of yours. So help me out. I mean... help. Almost 400 pages of hilarious fun. Time to show the public what a mind sharpened to dangerous sharpness by solving original problems can do. :-)))

 
Yurixx:

Anyway, Nikolai decided to make fun of me. He washed his hands of the issue and turned the tables on this thread.

I was not laughing. The first smiley meant self-irony, the second some scepticism. Or maybe joy that a real challenge has arisen and the thread is ready for it :)
 

Now you can't get away with it. Laughing wickedly and mockingly. You can see his teeth in the first smiley face. And in the second one, he's squinting so hard...

 
More seriously, I assume that the mean spread and RMS are related by a constant coefficient. This is why the diffusion formula (which deals with RMS) and the Hurst figure for random walk (which deals with the spread) have the same value, 1/2. For any particular implementation of any BP it can simply be directly calculated and it will, imho, be a good estimate. And the analytical conclusion is just for this branch of the problem.
 
If the value is not bounded (e.g. a normal distribution), then the spread will still have to be estimated somehow from some boundary probability. For example, take and define the spread as the difference between the percentiles 0.99 and 0.01. But percentiles are only calculated analytically in some exceptional cases of distributions.
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