Probability density function of successive intervals of a nonhomogeneous Poisson process under low-frequency conditions.

The probability density function (pdf) of successive intervals of a truncated, nonhomogeneous Poisson process was examined under both low- and high-frequency conditions. In general, if the instantaneous rate contains a single frequency component, then the phase of this component is not represented in the interval pdf. However, if the instantaneous rate contains harmonically related components, with fundamental frequency of the same order as, or less than, the mean rate, then the phases of these components do appear in the interval pdf. Correction formulae for estimating synchronization indices under low-frequency conditions are derived.