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Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

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DOI:

https://doi.org/10.52737/18291163-2018.10.5-1-20

Keywords:

normal distribution, central limit theorem, non-linear functional on several variables

Abstract

We introduce sufficiently wide classes of non--linear functionals preserving normal (Gaussian) distribution and establish various conditions under which a sequence of such functionals is asymptotically normal. As one of a consequence we obtain a generalization and sharpening of known results on the central limit theorem for weighted sums (linear functionals) of independent random variables.

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Published

2018-06-19

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How to Cite

Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality. (2018). Armenian Journal of Mathematics, 10(5), 1-20. http://test.armjmath.sci.am/index.php/ajm/article/view/175