Machine learning in trading: theory, models, practice and algo-trading - page 208
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Correct. Now let's calculate pgamma from 0+eps. What will it be equal to? Infinity because of dgamma(0,0.5,1)=inf. Right?
If you are looking for pgamma(0+eps, 0.5, 1) you should not compare with dgamma(0, 0.5, 1), but with dgamma(0+eps, 0.5, 1)
I've been answering just about that this morning, you missed it:
Let's take a simpler example:
x=1*10^(-90)
The number is very small, not zero, and there are no uncertainties.
Tungsten, the result is the same:
PDF[GammaDistribution[0.5,1], 1*10^(-90)]
5.6419×10^44
CDF[GammaDistribution[0.5,1], 1*10^(-90)]
1.12838×10^-45
Now, paraphrasing your question, without all the infinities in the formulas:
How can integrating dgamma, which returns big numbers like 5.641896e+44, result in a very small number1.128379e-45?
You must be satisfied that at X->0 dgamma will be very large, tending to infinity, while pgamma is very small tending to zero. This can be seen even in tungsten. How is it possible in this case that the integration gives a small result?
I took 1e-90 because tungsten can't do finer. In R you can look at the result at x=1e-300 - there will be a huge result in dgamma, and insignificant in pgamma.
And the only clue is that you're apparently trying to find pgamma by doing summation integration in a cycle with small steps, and Inf would really bother you. And R does it by some formula, not directly using the result of dgamma().
You are integrating something wrong somewhere.
I have searched for papers that mention the gamma density of the distribution at zero at different alpha & beta.
Here is one of them: http://journals.ametsoc.org/doi/pdf/10.1175/1520-0442(1990)003%3C1495%3AMLEFTG%3E2.0.CO%3B2
The researcher explicitly says that the density is maximized at point zero. And nothing, it lives, it doesn't suffer...
When Mr. Quantum admits that the error statement is an exaggeration or something else, that is, not correct, then my doubts about his professional competence will sort of dissipate. So far, I see religious arguments on his part and the head of MQ's part of his beneficence.
So far.
How do the developers of R explain their results:
dgamma(0,0.5,1)=inf
pgamma(0,0.5,1)=0
if they have point 0 included (as seen in the definition), gives infinite density at point x=0, and then when integrating into pgamma(x,0.5,1) infinity is considered as zero, as if it did not exist.
Now let's calculate pgamma from 0+eps. What will it be equal to? Infinity because of dgamma(0,0.5,1)=inf. Right?
http://www.wolframalpha.com/input/?i=integrate[pdf[gammadistribution[0.5,1],x]+,{x,0,1*10^(-90)}]
The integral is the area of the figure shaded in blue. As you can see, the left side of the shaded figure tends to infinity. Even though wolfram does not include the point x=0 in the pdf function, there is still no finite "highest point," you can think of the left side of the figure as growing up infinitely. Logically, if the left side of the figure grows up infinitely, then its area will also tend to infinity. But this doesn't actually prevent you from getting a non-infinite result when determining the area of that figure. Math.
5 pages of arguments about imaginary error in function that nobody needs in this thread, in the thread about machine learning, something is clearly wrong in this world...
You just can't read between the lines, you don't understand the hidden purpose of such pseudoscientific demagogy. Let me illustrate with a fictitious example.
Let's take, for example, oil production, let's assume that in narrow circles of successful oil producers gradually accumulates experience of research to find oil deposits on the basis of indirect, external signs, such as chemical composition of soil samples, vegetation pattern , etc. Naturally all this is kept in the strictest secrecy, and novice drillers are fed all sorts of TRUTHFUL information, something obvious with minor modifications, but not working, or even disinformation, which is difficult to check, except for trying and going bankrupt, with the help of "authorities". Time goes on, people are people, information gradually leaks and the time has come when it is already impossible to hide the technology in general terms, it became apparent and true, what to do?
The first thing that comes to mind, as in any game, when the enemy found out about the "secret technique" is all sorts of diversions aimed at complicating the comprehension of this secret knowledge, such as wetting his swamp of details, in a giant poorly structured stream of information which the brain is physically unable to digest and for 100 lifetimes, to take away from the essence , You want to understand how the Perspectron works, and you are recommended to understand number theory, at least at graduate school level, then mathematics, linear algebra, and all this is not in fact, but in detail, then you have to read all the papers, articles, etc. You want to read about how to develop a web application and you get tons of arguments about errors and programming patterns.
The second is all sorts of fakes, spoofing, when you cleverly moved to their field where the game is not by your rules. Do you need a perseptron? What "idiot" at the end of 2016 is going to write it himself? Ahahahaha)))) Cyclist disgraceful)))) There are tons of libraries out there! Buy a ferrari horse! Dig into other people's libraries and functions like a real "scientist"! You don't need to understand how and what is arranged there, you just need to go through the options that the developers have given you!
Well, so on and so on, I hope you understand what I mean :)
Play on your field and by your rules.
By the way, has anyone thought if Gamma and its related distributions can be used in the market? It is just a question...
ZZ trend length in bars by eye falls Poisson for small alphas. I didn't get into it more precisely, as I have no idea how to use it.
What do you mean, trend length distribution? Poisson is for the number of events per time delta. Or is it possible to stretch here as well? I just did not understand the physical context of the application...
We take the distance between ZZ reversals in bars and construct a histogram. Poisson to the eye.
On 13/11/2016 1:43 PM, Alexey Burnakov wrote:
It's the limit as x --> 0.
Using the limit is the most sensible method. Having a discontinuity in
the density will cause more problems, e.g. if the density is used in
quadrature.
As to the "correctness", we all know that the value of a density at any
particular point is irrelevant. Only the integrals of densities have
any meaning.
Duncan Murdoch