нормальний розподіл

Simulation of statistical mean and variance of normally distributed data $N_X(m_X,\sigma_X)$ transformed by nonlinear functions $g(X)=\cos X$, $e^X$ and their inverse functions $g^{-1}(X)=\arccos X$, $\ln X$

This paper presents analytical relationships for calculating statistical mean and variances of functions $g(X)=\cos X$, $e^X$, $g^{-1}(X)=\arccos X$, $\ln X$ of transformation of a normally $N_X(m_X,\sigma_X)$ distributed random variable.

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

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 for