M-estimation of Boolean models for particle flow experiments

Probability models are proposed for passage time data collected in experiments with a device that was designed to measure particle flow during aerial application of fertilizer. Maximum likelihood estimation of flow intensity is reviewed for the simple linear Boolean model, which arises with the assumption that each particle requires the same known passage time. M-estimation is developed for a generalization of the model in which passage times behave as a random sample from a distribution with a known mean. The generalized model improves the fit in these experiments. An estimator of total particle flow is constructed by conditioning on lengths of multiparticle clumps.