I.G. Karpov, D.K. Proskurin

Statistical property of display of properties of objects of the various nature, leading to fluctuations of measured sizes, and also presence not regular methodical and tool errors, use cause at the description and processing of experimental data of representations about them as about casual continuous or discrete sizes. The work purpose is working out of new forms of laws of distributions and kinds of numerical characteristics of the random variables providing, in particular, possibility of the generalized description of laws distribution of random variables and casual processes. Are offered: 1) differential function of distribution (DFD) the continuous random variable, representing a logarithmic derivative of function of density of distribution, and difference distribution function - analog DFD for a discrete random variable. Communication of the offered forms of laws of distribution with the equation of Pirsona and possibility of carrying out with their help of the generalized description of statistical properties of random variables is shown. A number of new numerical characteristics of continuous random variables, in particular, joint factor of asymmetry and an excess is considered. For symmetric distributions it coincides with factor of an excess and characterizes extent of distribution in comparison with extent of Gaussian distribution, and for asymmetrical distributions - in comparison with extent of reference gamma distribution. It can be used also at classification of bimodal distributions and distributions of other form which are distinct from the unimodal. In work are offered some more new numerical for more information on a continuous random variable.