Modelling skewness and kurtosis with the BCPE density in GAMLSS

Abstract

This paper illustrates the power of modern statistical modelling in understanding processes characterised by data that are skewed and have heavy tails. Our particular substantive problem concerns film box-office revenues. We are able to show that traditional modelling techniques based on the Pareto–Levy–Mandelbrot distribution led to what is actually a poorly supported conclusion that these data have infinite variance. This in turn led to the dominant paradigm of the movie business that ‘nobody knows anything’ and hence that box-office revenues cannot be predicted. Using the Box–Cox power exponential distribution within the generalized additive models for location, scale and shape framework, we are able to model box-office revenues and develop probabilistic statements about revenues.