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

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

MMC.
2022;
Volume 9, Number 2
: pp. 318–325
https://doi.org/10.23939/mmc2022.02.318
Received: August 17, 2021
Revised: February 01, 2022
Accepted: February 09, 2022

Mathematical Modeling and Computing, Vol. 9, No. 2, pp. 318–325 (2022)

Authors:
  1. P. S. Kosobutskyy
  2. M. S. Karkulovska
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

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.

statistical mean
variance
transformation
normal distribution
random variable
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