Karpov I.G., Evseesv V.V.

It is known, that the most full description of random variable (RV) is given by its law of distribution (density of probability, function of distribution or characteristic function). However frequently for description RV use their numerical characteristics which are turning out from the law of distribution over More often as numerical characteristics use the direct (positive) sedate moments. However sometimes use of the direct sedate moments does not enable to receive necessary quantity (amount) of the information reflecting all features of the law of distribution RV. Over the Basic purpose of the given work - to show, that for reception as it is possible a lot of the information on a random variable under numerical characteristics, necessary to use, alongside with straight linees, also the return sedate and logarithmic moments. Thus there is an opportunity to make more exact approximation both theoretical, and experimental distributions. In the beginning of work the elementary functional transformations of random variables at which there is a necessity of the reference to the return moments are established. Theorems by definition of the direct moments with use of the return moments for the transformed random variables are formulated and proved. Use of return and direct sedate alongside with the logarithmic moments allows to carry out classification of laws of distribution by presence at RV the direct and return moments. It is shown how to use the sedate and logarithmic moments for classification of a wide class of laws of distribution unilateral RV, the distributions represented by five types received by updating of equation Pearson and having generalizing character: , 0 < x < c ; (1) , 0 < x < ? ; (2) , 0 < x < ? ; (3) , 0 < x < ? ; (4) , c < x < ? , (5) where ? - 0, v - 0, c - 0 ? parameters of the form; ? - 0, ? - 0, ? - 0 - parameters of scale; B (a, b) ? бета-function; ? scale-function. It is established, as with the help of the direct, return and logarithmic moments to carry out approximation of experimental and theoretical laws of distribution RV with use of laws (1) ? (5). It has enabled to develop algorithm of the approached identification of laws of distribution of handicapes in radiochannels in conditions of aprioristic uncertainty.