A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we...

This tutorial gives an overview of SHAP (SHapley Additive exPlanation), one of the most commonly used techniques for examining a black-box machine learning (ML) model. Besides providing the necessary game theoretic background, we show how typical SHAP analyses are performed and used to gain...

The Gini index is the most commonly used measure of income inequality. Like any single summary measure of a set of data it cannot capture all aspects that are of interest to researchers. One of its widely reported flaws is that it is supposed to be overly sensitive to changes in the middle of...

This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable Y with a positive finite mean μY and the quantile function Q(x). The barycenter is denoted by μX and defined as the expected value of the random variable X having the...

This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable and explores its relation with the Gini index, the concentration area, and the Gini’s mean difference. The introduction of the barycenter allows for new economic, geometrical,...

Public questioning about the role of finance has been fuelled by the perception that financial sector pay is an important factor behind high economic inequalities. This paper is the first to provide a comprehensive look at the level of earnings in finance and the implications for labour income...

A key aspect defining the contemporary income distribution is the (increasing) share the top holds compared to the rest. This paper shows that income concentration increases towards the very top of the distribution, while the shares the middle- and upper-middle-income groups hold remain stable...