A Natural Simple Model of Scientists\u27 Strength Leads to Skew-Normal Distribution

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\u27 strength, this strength is skew-normally distributed. We also describe what happens if we consider more complex models of scientists\u27 strength