WORKSHOP ON RISK ANALYSIS AND APPLICATIONS
24 and 25 of SEPTEMBER, 2025
Institute of Mathematics and, Statistics of the University of São Paulo, Brazil
SATELLITE WORKSHOP OF
8th BRAZILIAN CONFERENCE ON STATISTICAL MODELING IN INSURANCE AND FINANCE
WORKSHOP ON RISK ANALYSIS AND APPLICATIONS
24 and 25 of SEPTEMBER, 2025
Institute of Mathematics and, Statistics of the University of São Paulo, Brazil
SATELLITE WORKSHOP OF
8th BRAZILIAN CONFERENCE ON STATISTICAL MODELING IN INSURANCE AND FINANCE
Title: A New Life of Pearson's Skewness
In this talk we attempt to rigorize the notion of Pearson's skewness. Informally, a probability distribution is positively skewed if its left half is "spreading short" and its right half is "spreading longer" and negatively skewed if vice versa. We use metric space centroids (i.e., Frechet means) to define generalized notions of positive and negative skewness that we call truly positive and truly negative. We apply the probabilistic methods of coupling and stochastic dominance for determining whether a continuous random variable is truly positively skewed. We present some basic examples of true positive skewness, thus demonstrating how the approach works in general.