Calculate the probability of reversal - page 7
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It is not the ways of estimating the parameters of a normal distribution (fitting, approximation) that show it at all. It is the normal distribution itself that does not have thick tails. Ask Alexander_K2, he was looking for those tails. Just look at the table with unit parameters. There are tables in every TV textbook, I think, and in every maths reference book. No matter how you adjust, you have to change the variant distribution to catch fat tails. And why do you need a distribution of type exactly? Exactly the probability distribution? Why these stamps for "some data"? Or is it not some data after all, but sampled relative frequencies, as I guessed?
Maybe the point is that the probabilistic representation does not describe your data at all? Remember, how the expected payoff dances on Yuriy Asaulenko's picture https://www.mql5.com/ru/forum/221552/page162#comment_6399653 on Forex rates. Don't you want to use the probabilistic representation for them? Then it is clear where the heavy tails come from.
Well of course, sample relative frequencies of price increments. I thought that was pretty clear, not many people are interested in the other options)
I don't use distributions for trading, just wanted to close knowledge gaps. Many practical nuances of matstat are not described in textbooks for some reason.
In this case, I'm not interested in distribution parameters, or even its type, but simply in the shape of the curve. How close it is to the Gaussian, where it deviates from it and by how much. There are hundreds of pages in textbooks about parameter estimation, and none about shape estimation.
What are you going to try, to reduce error? In formula formulation the problem set by you is solved in one line in general formulation, even comparison of results with your own experiment with k=0.65 is made. Or didn't you understand that p10^(1/10) is the solution?
Didn't read it carefully at first. The first thing that came into my head was the edge estimation, which is how I originally estimated it. But then a question arose, what if we take the central point of the histogram instead of the edges? And then I realized that it is not so simple, one degree is not enough. In any case, thanks for your participation, most likely I will solve the problem head-on, as always, by iterating and making a complete formula for each point of interest.
"by eye" means to plot the quantile-quantile(or probability-probability) plot for the sample and the normal distribution and make sure that it approximates the straight line well.
Well, it's going to be the same problem there. The absolute value of the error on the tails is many times smaller than in the centre. And the contribution should be the same, I assume.
I suspect this thread was not created by accident :)))
I recall that you somehow manage to reduce the double gamma-like distribution of increments in the market to pure normal... And now you're looking for an answer to the question - what's next!
I support Bas with his advice - you need to move into options. The Black-Scholes model should obviously work on your data.
Not really) what's next I decided a long time ago, even before I started doing. But I usually design algorithms somewhat in my own way, due to my limited knowledge of mathematics, they often consume a lot of resources, and solve the problem in specific ways.
Sometimes I'll do something, and then some time later I'll find solution, which turns out to be much easier and more economical.
That is, I still want to evolve and take a smarter approach each time.
As for the Black-Scholes model, when I first heard about it, I was very surprised that they gave a Nobel Prize for such a primitive model and I thought: "I see where the market science is at the bottom", I used a similar technology in my old developments, but I did not know that they give out Nobel Prizes for that)). Now I know where the mistakes are and if I go to trade options, it's not with this formula.Well, it's going to be the same problem there. The absolute value of the error at the tails is many times less than at the centre. And the contribution should be the same, as I assume.
We should look at how these errors are distributed over time in the initial sample and if there is no dependence between them. If there is no dependence and they are located more or less evenly, we must select another parametric family of distributions. Otherwise, the conditions of Glivenko-Kantelli theorem are violated and one should not hope that the histogram approximates the density of some distribution.
It is necessary to see how these errors are distributed over time in the original sample and if there is no dependence between them. If there is no dependence and they are more or less evenly distributed, we must choose another parametric family of distributions. Otherwise the conditions of Glivenko-Kantelli theorem will be violated and we should not hope that the histogram approximates the density of some distribution.
The question is whether I'm doing it correctly, giving the errors in the tails the same weight as in the centre (using the above mentioned two methods that I had to invent myself due to their absence in the textbooks).
I am not interested in a particular kind of distribution. Only differences from Gaussians are of interest.
The question is whether I am doing the right thing by giving the errors in the tails the same weight as the errors in the centre (using the above two methods, which I had to invent myself due to their absence in the textbooks).
I am not interested in a particular kind of distribution. Interested only in differences from the Gaussians.
Let's consider a graph of uniform distribution density on the interval from zero to one. Gaussians with what parameters will correctly approximate it?
A counter question - let's have a graph of the density of a uniform distribution on a segment from zero to one. What parameters of the Gaussian will correctly approximate it?
Well, we are talking about distributions that look like a Gaussian.
Well, we're talking about distributions that look like a Gaussian.
OK, let's take a Cauchy or Laplace distribution density then.