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.

Keywords:

• clumpiness
• test statistics
• media consumption

Notes

‘The Year in TV – The 2008 Culture Awards’ New York Magazine, December 2008 (accessed 31 July 2011) (Available at http://nymag.com/arts/cultureawards/2008/52737/index1.html).

GVT was introduced in Section 1, which refers to three articles as a group.

Supplementary content may be viewed online at http://dx.doi.org/818627.

For i=2, …, n, ; x ₁=t ₁ and x _n+1=N−t _n . It follows that .

If the last event occurs at the end of observation period, there is a problem of taking the logarithm of zero. We set x _n+1 equal to 1 instead of 0 to avoid this problem. This adjustment is reasonable since the special case rarely happens (2% of the time in our Hulu.com example), and also it does not make a significant difference after being scaled by N.

Here 0.05 was chosen as the threshold.