normal distribution

STATISTICAL VALIDATION OF THE AMPLITUDE VARIABILITY MODEL OF ELECTROCARDIOGRAPHIC SIGNAL

This study conducted comprehensive validation of the mathematical model of the discrete amplitude variability function for characteristic electrocardiographic wave peaks using clinical data from patients with myocardial ischemia, supraventricular arrhythmia, ventricular tachycardia, and normal sinus rhythm. The research investigated the stationarity of the amplitude variability function using the Augmented Dickey-Fuller test and distribution normality using the Anderson-Darling test on electrocardiogram recordings from the PhysioNet database.

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