Discussion of article "Fundamentals of Statistics" - page 2

[GaryKa]

Yurich: The standard deviation is differentiated in contrast to the absolute mean. This, in turn, makes it possible to use this function in further analytical calculations, for example, in the method of least squares. There are other advantages as well.

I have heard about one more advantage - the standard deviation is more sensitive to emissions. So let's unite the whole world, and go to promote not the square of the difference, but for example the difference in the fourth degree. Such average "quaternary" deviation is surely also differentiated and even more sensitive to outliers than the standard deviation.

In my opinion, the square of the difference follows, as Rosh has already said, from the"property of the algebra of our space ", namely from the metric of linear space (distance between vectors). But who said that all samples belong to linear space.

hrenfx: Other norms of errors are quite admissible.

Of course they are allowed. The question is when and why to use such estimates. In discussions somehow more often there are affirmative phrases like"but he went beyond bollinger with one sko ". Why the sko? Why one? I guess you like the 68% figure.)

[GaryKa]

QSer29: ... 1,2) Some mathematical calculations explaining the use of arithmetic mean and standard deviation - http://teorver-online.narod.ru/teorver49.html .

And here is an example on your fingers from the resource you mentioned. The mathematical expectation of the number that fell out on the top edge of an ordinary dice. If you calculate it as an arithmetic mean, it's 3.5.

What does that number mean to you?

What would this number be and what would be its meaning if:

• if you put 100 more dots on a face with 6 dots on it.
• put a letter on one of the faces instead of dots.
  

Imho all these estimations of expectation and deviation through the arithmetic mean and sco are a bit over the ears to the uniform and therefore to the normal distributions.

[hrenfx]

GaryKa:

I have heard about one more advantage - standard deviation is more sensitive to emissions.

Absolutely right, so it is desirable to justify the choice of the error rate in some way. For example:

The use of RMS (standard deviation) instead of WMS (modulo-mean deviation) is caused by the necessity to give more importance to the distant outliers of QC values from its MO (mat. expectation).

One can also use the biquadratic norm of error. In the general form Abs(Func(Error)). However, a great number of analytical solutions and algorithms with excellent efficiency have been developed precisely for the quadratic norm, which is remarkable in its properties (from the matrix point of view).

[QSer29]

GaryKa:

Here is an example from the resource you mentioned. The mathematical expectation of the number falling on the top edge of an ordinary dice. If you calculate it as an arithmetic mean, it's 3.5.

What does that number mean to you?

What would this number be and what would be its meaning if:

• if you put 100 more dots on a face with 6 dots on it.
• put a letter on one of the faces instead of dots.
  

Imho all these estimations of the expectation and deviation through the mean and sko are a bit of a stretch for uniform and therefore normal distributions.

I gave a link to another page from this resource to answer specific questions.

When we deal with a dice, we deal with a random variable, and its parameters should be estimated not as samples. In this case, the expectation of a random variable (the die) is 3.5. Mat. expectation of a discrete random variable is calculated by a different formula in contrast to the arithmetic mean. In this case, these values just coincided, because the probability of falling out of each side of the die is the same.

• you calculate by the formula of expectation matrix for a discrete random variable with the same probability of falling sides for a cube with a new face.
• Here we can no longer talk about the expectation of a random variable.

[secret]

hrenfx:
The original problem?

Simple as a rake - modes show the levels of "price concentration" relative to the approximation line. But to use them, one must first know that they exist at all.

[secret]

I've heard of another advantage - the standard deviation is more sensitive to emissions.

Is that an advantage?

[hrenfx]

There should be plenty of algorithms for determining mods, so a universal bicycle is not useful here.

You should rather look at examples, what you want to get and what you don't want to get.

[Andrey Khatimlianskii]

I liked the article.

It is very easy to understand and contains enough information.

And, judging by the title, it doesn't pretend to be more than that.

[СанСаныч Фоменко]

I don't see any use for this article. A number of platitudes from TV. And if this article was not printed on a specialised, half-trader website, it would be possible to keep silent. But considering the site, I would like to note the following.

There is a science of measuring, analysing and forecasting economic data. It is called econometrics. It is a close, blood relative of statistics, but there are significant differences.

1. For traders, the analysis itself has no value if the forecast does not follow from the analysis. The article does not mention forecasting at all.

2. Econometrics initially proceeds from the non-stationarity of economic series. And if one would at least remember about it, keep it in mind, so to speak, the story about basic statistics would not be so rosy: for non-stationary series the basic concepts of mo, variance, etc. can be applied with a lot of reservations. At any rate one should always be in doubt. For example, for non-stationary series, the mean will not necessarily converge to the mo. I am not talking about correlation at all.

3. econometrics is based on very short samples - a few dozens of observations. It is not interested in the average for many years, since such an average also implies being in a pose for several years. In crises, estimates of the results of the calculation become important. It is the estimates that radically distinguish TV from statistics and especially from econometrics.

School article. The level of a special school, not even junior courses of an institute.

[runk]

Thanks for the article. Small correction - the chapter "Selective Asymmetry" in the formula the degree of dispersion is 3/2, not 2/3. :)