BurstinessParameter

BurstinessParameter is a dimensionless metric used to quantify how much the timing of events in a sequence deviates from a random, Poisson-like process. It is commonly applied to time-stamped data such as human activities, communication events, or neuronal spike trains to capture the tendency of events to cluster into bursts versus occurring at a steady pace.

Formally, for a sequence of inter-event times τi, compute the mean μ = E[τ] and the standard deviation σ = STD[τ]. The BurstinessParameter is defined as B = (σ − μ) / (σ + μ). The value of B typically lies in the interval [-1, 1], though practical estimates may exceed slightly due to finite-sample effects. Larger values indicate stronger burstiness (more clustering of events), while smaller values indicate more regular or Poisson-like behavior. A value near 0 corresponds to randomness with no pronounced burstiness.

Computation and interpretation considerations: B is scale-invariant to time units, since scaling all inter-event times by a constant factor cancels in the formula. It is sensitive to the length of the observation window and to non-stationarities in the data. Finite sample size can bias estimates, especially with few events or highly variable τi. In practice, B is often complemented with the full inter-event time distribution or with multi-scale analyses to capture complex burstiness patterns.

Applications and limitations: BurstinessParameter is used in studies of human dynamics, communication networks, and neuroscience to compare activity patterns across individuals or conditions. It does not capture multi-scale bursts or memory effects on its own; it summarizes overall dispersion of inter-event times.