Why is the normal distribution not normal?
I've heard many times about the thick tails of the distribution, but I still do not understand what the point is. I made an indicator which outputs the bar size distribution (plotted on Close[i]-Close[i+1] difference) to separates, can someone explain why the distribution is narrower than normal?
Actually, it should be higher and narrower. This is because it is the property of price repayment that affects it.
What do you mean already ?
>> already
The main and only condition to get HP is independence of the terms of the series. This is the proof that independence is not fulfilled.
It's kind of not quite normal. :) This has already been discussed in intuition. They say it's an Erlang distribution. And they say there's no tails, but there should be. :)
I was talking about Erlang, but that's not the issue here. The normal distribution has 2 parameters - MO and variance. In this case MO = 0, but the variance is not zero and in order to draw a graph we need to set its value. So I'm asking, how did Urain choose the variance value?
And in general, in order to compare graphs, they must somehow be reduced to a common basis. Depending on the choice of this base, there can be completely different patterns.
If we take the variance as this common basis, the graph will be narrower, but thick tails will appear.
I was talking about Erlang, but that's not the issue here. The normal distribution has 2 parameters - MO and variance. In this case MO = 0, but the variance is not zero and in order to draw a graph we need to set its value. So I'm asking, how did Urain choose the variance value?
In general, in order to compare graphs, they must somehow be reduced to a common basis. Depending on the choice of this base, there can be completely different patterns.
If we take the variance as this common basis, the graph will be narrower, but thick tails will appear.
I strongly suspect that Urain took similar characteristics of the resulting series as input parameters for expectation and variance. But maybe this is not the case.
The main and only condition to get HP is independence of the terms of the series. This is the proof that independence does not hold.
A mechanical light bulb production line is likely to have a normal distribution of REAL random failures, equipment errors. Therefore, it is likely that the number of normally produced bulbs (their brightness, resistance, filament thickness) will fit into a normal distribution curve. On the sides of this normal curve (its thin tails), there will be BORDER cases where the filament thickness is above or below the standard and the bulb burns out. But the total number of such borderline, abnormal cases can be calculated in advance (by integrating the distribution curve or whatever). This is why the light bulb factory knows in advance that a box of bulbs might contain an average of three bad bulbs which will burn out in the very near future. They have to be replaced under warranty, so the local bulb distributor, in faith in the science of statistics, reports an average of 3 extra bulbs per case. The errors in the bulb parameters fall within the NORMAL LOCAL EVENT CRIVE (not the parameters themselves, but their errors). The random event here is not the release of the bulb itself, but the ERROR of the bulb parameter.
If the process of bulb production (or more exactly the formation of the bulb parameters) does not fit into a normal curve, e.g. the line is broken and it is defective, the supplier has sent bad tungsten, then the defect rate will increase dramatically, the bulb parameters will "stray". If one then measures accurately the parameters of a batch of bulbs, they will not fit into the curve of norms. In this case the plant does not know how many bulbs it has to deliver to the distributor.
If we measure a non-random process, then... you can't say anything at all. You can plot the probability distribution curve of an event - simply by measuring the occurrence of the event within an interval, but... it doesn't tell us anything.
Electrical engineers and the mathematicians and statisticians they employ LOVE to deal with measurement errors. Which are most likely NORMAL (if the device itself was made by a normal engineer). Hence all their formulas.
For price series, first differences (or other combinations) are not a random event, and their distribution curve MAY BE ANYTHING. And even if it is known precisely, it is of no use for trading.
Don't pick on me, I had a 2 in both theory and matstat.
So, candlestick analysis can work with 60-40 or even 70-30 probability. This is good.
Dependencies can be very different. It doesn't necessarily depend on the values of previous increments, which is what candlestick analysis does. It can be, for example, dependence on the modulus of the value of increments (volatility). The fact that volatility is autocorrelated is well known and volatility models such as GARCH (using autocorrelation) have received a Nobel Prize. It's not difficult to see it for yourself. And this is one of the variants why the distribution has "heavy tails".
P.S. In a broad sense, independence is described in the definition of stationarity.
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I've heard many times about thick tails of distribution, but I still do not understand what the point is, I made an indicator which outputs bar size distribution (based on Close[i]-Close[i+1] difference) into separates, can someone explain why distribution of bars is narrower than normal?
The benchmark is a red line yellow histogram.
And the indicator that was used to build it. Original title (Distribution_GCF_&_norm_test)