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Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality
DOI:
https://doi.org/10.52737/18291163-2018.10.5-1-20Keywords:
normal distribution, central limit theorem, non-linear functional on several variablesAbstract
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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2018-06-19
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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