Power Laws and Skew Distributions: An Application to Performance Royalty Income

Abstract

Royalty income derived from copyrighted song-titles is often highly skewed. This skewness, in which a relatively small number of songwriters earn relatively more royalty income than other members or affiliates in Performing Rights Organizations, is said to follow Zipf's Law or a Pareto distribution. Skewness in royalty income can be explained, in part, by some successful songwriters having larger catalogs of songs that are performed more frequently by radio stations, television stations, and other public places, such as retail outlets, bars, restaurants and clubs. The skew-t distribution model is generalized with location, skew, scale, and degrees of freedom parameters and is used to analyze royalty income when skewness and heavy-tails (outliers) are present. The multivariate log-skew-t maximum likelihood model presented here provides a better fit over other methods when the normal (Gaussian) assumptions and graphical methods may be inappropriate.