A Natural Simple Model of Scientists' Strength Leads to Skew-Normal Distribution

Authors

Komsan Suriya, Chiang Mai UniversityFollow
Tatcha Sudtasan, Chiang Mai UniversityFollow
Tonghui Wang, New Mexico State University - Main CampusFollow
Octavio Lerma, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

2-2015

Comments

Technical Report: UTEP-CS-15-14

Abstract

In many practical situations, we have probability distributions which are close to normal but skewed. Several families of distributions were proposed to describe such phenomena. The most widely used is skew-normal distribution, whose probability density (pdf) is equal to the product of the pdf of a normal distribution and a cumulative distribution function (cdf) of another normal distribution. Out of other possible generalizations of normal distributions, the skew-normal ones were selected because of their computational efficiency, and not because they represent any real-life phenomena. Interestingly, it turns out that these distributions do represent a real-life phenomena: namely, in a natural simple model of scientists' strength, this strength is skew-normally distributed. We also describe what happens if we consider more complex models of scientists' strength.