Divided statistics and their application. Kudlaev E.M.

The monograph refers to a promising direction and is devoted to a systematic study of the divided statistics (PC) - the sums of functions of random arguments: arguments are assumed dependent in such a way that there are independent random values ​​in some probabilistic space, the conditional distribution of which coincides with the joint distribution of random arguments, provided fixation of their amount. This systematization contributes to the assumption that the values ​​of random arguments and functions from them belong to switching topological groups. Separate results related to the amounts of this kind have been known for a long time.

in the last few decades, interest in PC has increased extremely, which was reflected in the appearance of hundreds of publications and monographs.

The main part The results of the monograph belongs to the author and compiles: the theorem of existence, the classification of PC, the weak convergence (with an increase in the number of terms) distributions of PC, including in continual alternatives, which is important for the tasks of mathematical statistics - criteria for consent and homogeneity, tasks with the Neumanza structure. Generalizations of divided statistics are given.

for students, graduate students and specialists in probability theory and its applications.