Burstiness parameter for finite event sequences

Characterizing inhomogeneous temporal patterns in natural and social phenomena is important to understand underlying mechanisms behind such complex systems, hence even to predict and control them. Temporal inhomogeneities in event sequences have been described in terms of bursts that are rapidly occurring events in short time periods alternating with long inactive periods. The bursts can be quantified by a simple measure, called burstiness parameter, which was introduced by Goh and Barab\'asi [EPL \textbf{81}, 48002 (2008)]. The burstiness parameter has been widely used due to its simplicity, which however turns out to be strongly biased when the number of events in the time series is not large enough. As the finite size effects on burstiness parameter have been largely ignored, we analytically investigate the finite size effects of the burstiness parameter. Then we suggest an alternative definition of burstiness parameter that is unbiased and yet simple. Using our alternative burstiness parameter, one can distinguish the finite size effects from the intrinsic bursty properties in the time series. We also demonstrate the advantages of our burstiness parameter by analyzing empirical datasets.