Calculate the probability of reversal - page 8
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OK, let's take a Cauchy or Laplace distribution density then.
I'm not interested in Cauchy or Laplace distribution, and I don't plan to set it)
And I don't need Gaussian parameters. The question is different.
... How close it is to the Gaussian, where it deviates from it and by how much ...
I just wanted to understand how you would answer this question in the hypothetical case where it is known that the data are distributed exactly according to the standard Cauchy distribution. Then it would be easier to answer in the case of real data as well. For example, something along the lines that we take that Gaussian for which the sum of moduli of deviations of deciles is minimal, etc.
Or I don't understand the question at all.
I just wanted to see how you would answer this question in the hypothetical case where you know for sure that the data are distributed exactly according to the standard Cauchy distribution. Then it would be easier to answer in the case of real data as well. For example, something along the lines that we take that Gaussian for which the sum of moduli of deviations of deciles is minimal, etc.
Or I don't understand the question at all.
Alexey, how can the analogy of Cauchy distribution be applied in practice?
Interesting postscript, it did not come through
I just wanted to see how you would answer this question in the hypothetical case where you know for sure that the data are distributed exactly according to the standard Cauchy distribution. Then it would be easier to answer in the case of real data as well. For example, something along the lines that we take that Gaussian for which the sum of moduli of deviations of deciles is minimal, etc.
Or I don't understand the question at all.
Well, the usual linear approximation by MNC. We take the Gaussian for which the sum of squares of deviations is minimal.
The question is that in the centre of the distribution the value of deviations will be, say, of the order of 0.1. And on the tails, let us say, of the order of 0.01.
I.e. the fitting will occur mostly at points from the centre of the distribution.
And it seems to me that all points should participate equally.
For this you can either take a logarithmic scale on the vertical axis, or instead of deviation-differences take deviation-partial, i.e. divide one distribution by another, and then already approximate.
Well, the usual linear approximation by ANC. We take the Gaussian for which the sum of the squares of the deviations is minimal.
The question is that in the centre of the distribution the value of the deviations will be, say, of the order of 0.1. And on the tails, let us say, of the order of 0.01.
I.e. the fitting will occur mostly at points from the centre of the distribution.
And it seems to me that all points should participate equally.
To do this you can either take a logarithmic scale on the vertical axis, or take deviation-partial instead of deviation-differences, i.e. divide one distribution by another, and then already approximate...
Is there any reason why the "participation" of points that occur rarely should nevertheless be the same as that of points close to the median (centre) that occur much more frequently? Why such a role amplification in the approximation? Wouldn't it come out that "the tail wags the dog"?
Actually, there are MNCs with weights to control the role of different points. For example, assign them as values inverse to probability density function of normal distribution and that's it. The main thing is to keep the sum of the weights to 1. By the way, what is "linear approximation by MNC" if not a straight line approximation?
Is there any reason why the 'participation' of points that occur rarely should nevertheless be the same as that of points close to the median (centre) that occur much more frequently? Why such a strengthening of the role in the approximation? Wouldn't it come out that "the tail is wagging the dog"?
Actually, there are MNCs with weights to control the role of different points. For example, set them as values inverse to probability density function of normal distribution and that's it. The main thing is to keep the sum of the weights to 1. By the way, what is a "linear" MNC?
1. Of course there is. The tails are of a large magnitude, after all. Applied to the market - rare but large losses. It's not role reinforcement, it's compensation for the lack of role, resulting in giving equal roles to all points.
2. About MNC with weights I know. The issue is not the approximation technique, but its ideology.
3. When a linear relationship is assumed between quantities.
1. Of course there are. There are big tails, after all. Applied to the market, rare but large losses.
2. I know about MNC with weights. The question is not in the approximation technique, but in its ideology.
3. When a linear relationship is assumed between values.
1. This is no longer a probabilistic approach. The tails of the probability distribution mean small, rare cases, while the main, significant ones have their own distribution, rapidly decreasing towards the edges.
2. The question was: "By the way, Alexey, and Vladimir, tell me. Suppose we want to approximate some data by normal distribution.Tails and middle of distribution should have the same weight in approximation, I suppose?"
The answer is no. If we model the problem with probabilistic methods, then of course those events that occur more often than others are more important, i.e. more likely. This is ideological.
3. linear causality, you mean? Does the ISC care what kind of relationship there is?
Well, the usual linear approximation by ANC. We take the Gaussian for which the sum of the squares of the deviations is minimal.
The question is that in the centre of the distribution the value of the deviations will be, say, of the order of 0.1. And on the tails, let us say, of the order of 0.01.
I.e. the fitting will occur mostly at points from the centre of the distribution.
And it seems to me that all points should participate equally.
To do this, one can either take a logarithmic scale on the vertical axis, or instead of deviation-differences take deviation-partial, i.e. divide one distribution by another, and then already approximate it.
It is somewhat reminiscent of Pearson's goodness-of-fit test (chi-square). Have a look at Kobzar in chapter three. It is only necessary to clearly understand the difference between the simple null hypothesis and the complex hypothesis, when the distribution parameters are unknown and are estimated from the sample (for example, by minimizing the chi-square statistic).
1. This is no longer a probabilistic approach. The tails of the probability distribution refer to small, rare cases, and the major, significant ones have their own distribution, rapidly decreasing towards the edges.
2. The question was: "By the way, Alexey, and Vladimir, tell me. Suppose we want to approximate some data by normal distribution.Tails and middle of distribution should have the same weight in approximation, I suppose? "
The answer is no. If we model the problem with probabilistic methods, then of course those events that occur more often than others are more important, i.e. more likely. This is ideological.
3. linear causality, you mean? Does the ISC care what kind of relationship there is?
1. they are NOT insignificant. One such "minor" case could result in the loss of everything earned by the "major" ones.
3. a linear correlation relationship. MNC all the same, linear I called approximation, not MNC.
Somewhat reminiscent of Pearson's goodness-of-fit test (chi-square). See Kobzar in chapter 3. It is only necessary to clearly understand the difference between the simple null hypothesis case and the complex one, when the distribution parameters are unknown and are estimated from the sample (for example, by minimizing the chi-square statistic).
Well, there is no task to estimate distribution parameters)