Of Two Evils Choose the Least

There are more mathematicians in the world than successful traders. This fact is often used as an argument by those opposing complex calculations or methods in trading. We can say against it that trading is not only ability to develop trading rules (analyzing skills), but also ability to observe these rules (discipline). Besides, a theory that would exactly describe pricing on financial markets have not been yet created by now (I think it will never be created). The creation of the theory (discovery of mathematical nature) of financial markets itself would mean death of these markets which is an undecidable paradox, in terms of philosophy. However, if we face the question of whether to go to the market with not quite satisfactory mathematical description of the market or without any description at all, we choose the least evil: We choose methods of estimation of trading systems.

What is Abnormality of Normal Distribution?

One of basic notions in the theory of probability is the notion of normal (Gaussian) distribution. Why is it named like this? Many natural processes turned out to be normally distributed. To be more exact, the most natural processes, at the limit, reduce to normal distribution. Let us consider a simple example. Suppose we have a uniform distribution on the interval of 0 to 100. Uniform distribution means that probability of falling any value on the interval and probability of that 3. 14 (Pi) will fall is the same as that of falling 77 (my favorite number with two sevens). Modern computers help to generate a rather good pseudorandom-number sequence.

How can we obtain normal distribution of this uniform distribution? It turns out that, if we take every time several random numbers (for example, 5 numbers) of a unique distribution and find the mean value of these numbers (this is called 'to take a sample') and if the amount of such samples is great, the newly obtained distribution will tend to normal. The central limit theorem says that this relates to not only samples taken from unique distributions, but also to a very large class of other distributions. Since properties of normal distribution have been studied very well, it will be much easier to analyze processes if they are represented as a process with normal distribution. However, seeing is believing, so we can see the confirmation of this central limit theorem using a simple MQL4 indicator.