Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

Linda Khachatryan

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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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Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

Abstract

Author(s)

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Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

Abstract

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