  Fluctuation scaling has been observed universally in a wide variety of
phenomena. In time series that describe sequences of events, fluctuation
scaling is expressed as power function relationships between the mean and
variance of either inter-event intervals or counting statistics, depending on
measurement variables. In this article, fluctuation scaling has been formulated
for a series of events in which scaling laws in the inter-event intervals and
counting statistics were related. We have considered the first-passage time of
an Ornstein-Uhlenbeck process and used a conductance-based neuron model with
excitatory and inhibitory synaptic inputs to demonstrate the emergence of
fluctuation scaling with various exponents, depending on the input regimes and
the ratio between excitation and inhibition. Furthermore, we have discussed the
possible implication of these results in the context of neural coding.
