A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables

Abstract

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Entropy-metric estimation of the small data models with stochastic parameters

“…The structural properties of functions and are regulated by their class. To determine the latter in the context of , the optimization problem [ [20] , [21] , [22] ] should be solved, and in the context of , the optimization problem [ 20 , 21 , 23 ] should be solved. In both cases, these are stochastic linear programming problems with probabilistic equality constraints [ 34 , 35 ].…”

“…We have already mentioned the hypothesis that a data sample summarizes Independent and Identically Distributed (IID) values [ [20] , [21] , [22] , [23] ], characteristic of both machine learning and mathematical statistics. For a large test sample, such an estimate will be quite accurate.…”

Novel Successive Interference Cancellation (SIC) With Low-Complexity for GFDM Systems

“…As shown in this figure the distributions are Gaussian and the analytical results match well with that of the simulations. Mathematically, the results are justified according to the central limit theorem [33]. The complex Gaussian approximation of the self-interference factor can be expressed as follows:…”