Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions $\sqrt{|X|}$ and $\sqrt{X}$

Abstract

This paper presents theoretical studies of formation regularities for the statistical mean and variance of normally distributed random values with the unlimited argument values subjected to nonlinear transformations of functions $\sqrt{|X|}$ and $\sqrt{X}$. It is shown that for nonlinear square root transformation of a normally distributed random variable, the integrals of higher order mean $n>1$ satisfy the inequality $\overline{(y-\overline{Y})^n}\neq 0$. On the basis of the theoretical research, the correct boundaries $m,\sigma \to \infty$ of error transfer formulas are suggested.