So, for example, on the purchase of security allows him a proprietor to get an income in the case of positive profitableness and at the same time avoid losses in the case of subzero, I.e. in fact, chops off distributing of profitableness in a point, where losses begin.

Chart of closeness of distributing of probability with right asymmetry.

In parallel instances the use in the process of analysis only of two parameters (middle and standard deviation) can result in incorrect conclusions. Standard deviation inadequately characterizes a risk at the displaced distributing, as ignored, that greater part of changeability is on the «good» (right) or «bad» (left) side of the expected profitableness. Therefore at the analysis of the asymmetric distributing use an additional parameter – coefficient of asymmetry (slant). He is the rationed size of the third central moments and determined on a formula:

Economic sense of coefficient of asymmetry in this context consists in the following. If a coefficient has a positive value (positive slant), then the highest profits (right «tail») are considered more credible, than low and vice versa.

The coefficient of asymmetry can be also used for approximate verification of hypothesis about normal distribution of casual size. His value in this case must be equal to 0.

Distributing displaced in a number of cases to the right it is possible light to normal addition 1 to the expected size of profitableness and by the subsequent calculation of natural logarithm of the got value. Name such distributing . It is used in a financial analysis along with normal one.

Some symmetric distributing can be characterized the fourth rationed central moments – excess (е):

If value of excess more than 0, a distribution curve is more pointed, than normal curve and vice versa.

Economic sense of excess consists in the following. If two operation have symmetric allocations of profits and identical middle, the less risky is consider an investment with a large excess.

For normal distribution an excess is equal to 0.

Use normal distribution, when it is impossible exactly to define probability that a continuous casual size takes on some concrete value. Normal distribution supposes that the variants of the forecast parameter gravitate to the mean value. The values of parameter are substantially different from middle, I.e. being in “tails” distributing, have small probability of realization. Such is nature of normal distribution.

The three-cornered distributing is a substitute normal and the distributing supposes arcwise increasing as far as approaching to the fashion.

The трапециевидное distributing supposes the presence of interval of values with most probability of realization (NVR) within the limits of RVD.

The even distributing gets out, when it is assumed that all variants of the forecast index have identical probability of realization.

However, when a casual size is discrete, but not continuous, apply the binomial distributing and distributing of Puassona.