Statistical series for the ordered array approximation of random variable

Many papers contain the study of observation results by using statistical moments and signs of the shape of distributions of random variables. Most of the directions of the application of moments are based on the relationship of moments with the parameters of the shape and scale of distributions. Expansion of the boundaries for the distribution parameters area is possible by identifying new qualitative properties of these characteristics. For this reason, it is relevant to study the possibility of using the central moments of the n-th order when constructing a statistical series. The paper demonstrates the possibility of using distribution moments to construct a series of approximations of a sorted data sequence. In particular, a method is developed for the expansion of a monotone varying function in a power series, that it is based on obtaining the coefficients of the series by using the central moments of the n-th order which calculated from a random sample of data. There are also examples of sorted series approximation for typical known symmetric and asymmetric distributions. There are also examples of sorted series approximation for typical known symmetric and asymmetric distributions. The article illustrates the use of a statistical series for the study of arrays of random variables by the example of approximating a sorted sequence of one cycle of an electrocardiosignal.