The paper provides information about the distribution laws of continuous random variables and shows how they can be identified using double symbols: Latin or Greek letters. It also includes a frequency diagram in the «asymmetry – excess» coordinates, where these laws are represented as points, curves, and regions, which helps to speed up the selection of distribution laws that match the sample of random variables being studied.It is shown that the most universal is the 1st kind β-distribution, characterized, as well as a sample of random variables, by four indicators: the mean and coefficients of variation, asymmetry and excess. Analytical expressions are given, allowing to determine the parameters of the 1st kind β-distribution by the above-mentioned indicators of the random variable sample, as well as the limitations of the applicability of the 1st kind β-distribution. Examples of finding the parameters of the 1st kind β-distribution for various samples of random variables are given, which may be of interest for specialists of EMERCOM of Russia.
Tarantsev et al. (Fri,) studied this question.