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  4. 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 $g^{-1}(X)=\arccos X$, $\ln X$

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 $g^{-1}(X)=\arccos X$, $\ln X$

MMC.
2023;
Volume 10, Number 4
: pp. 1014–1022
https://doi.org/10.23939/mmc2023.04.1014
Received: January 14, 2023
Revised: November 15, 2023
Accepted: November 16, 2023

Mathematical Modeling and Computing, Vol. 10, No. 4, pp. 1014–1022 (2023)

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

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.

statistical mean
variance
transformation
normal distribution
random variable
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