The application of multipoint statistics to the analysis of sprays and other particle flows is extended in order to encompass third- and higher-order statistical information. The relationships between data taken from (e.g.) phase Doppler measurements of particle arrival times and the intensity function which represents a particle flow are investigated. It is shown that, at any order, the distribution of all gaps between particle arrival times has a more direct relation to the correlation functions which characterize the flow than does the distribution of sequential interparticle times. Moments of the intensity distribution are expressed in terms of the behavior of the distributions for small interparticle gaps. Examples of stochastic intensity functions are given to illustrate the significance of differences in higher-order correlations.