Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables

Abstract

Random variables in biology, social and health sciences commonly follow skewed distributions. Many of these variables can be represented by exGaussian functions; however, in practice, they are sometimes considered as Gaussian functions when statistical analysis is carried out. The asymmetry can play a fundamental role which can not be captured by central tendency estimators such as the mean. By means of Monte Carlo simulations, the effect of a small asymmetry in the generating functions of the chi distribution is studied. To this end, the k generating functions are taken as exGaussian functions. The limits of this approximation are tested numerically for the practical case of three health-related variables: one physical (body mass index) and two cognitive (verbal fluency and short-term memory). This work is in line with our previous works on a physics-inspired mathematical model to represent the reaction times of a group of individuals.

Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System

“…,18. In what follows, we will establish, by means of a Monte Carlo study [28,29], which conditions must be satisfied by the parameters defining the matrix A and the vector b so that the Lotka-Volterra equation has a single asymptotically stable equilibrium point with all its positive (and non-zero) coordinates.…”

Editorial of Special Issue “Application of Mathematical Modelling and Symmetry in Neuroscience”

“…The second article is "Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables" [6]. In nature, it is difficult to find a symmetric distribution.…”