New measures of clumpiness for incidence data

Abstract

In recent years, growing attention has been placed on the increasing pattern of ‘clumpy data’ in many empirical areas such as financial market microstructure, criminology and seismology, and digital media consumption to name just a few; but a well-defined and careful measurement of clumpiness has remained somewhat elusive. The related ‘hot hand’ effect has long been a widespread belief in sports, and has triggered a branch of interesting research which could shed some light on this domain. However, since many concerns have been raised about the low power of the existing ‘hot hand’ significance tests, we propose a new class of clumpiness measures which are shown to have higher statistical power in extensive simulations under a wide variety of statistical models for repeated outcomes. Finally, an empirical study is provided by using a unique dataset obtained from Hulu.com, an increasingly popular video streaming provider. Our results provide evidence that the ‘clumpiness phenomena’ is widely prevalent in digital content consumption, which supports the lore of ‘bingeability’ of online content believed to exist today.