M-estimation of Boolean models for particle flow experiments

TL;DR

This paper develops M-estimation methods for Boolean models to analyze particle flow data, improving model fit and estimating total flow in aerial fertilizer application experiments.

Contribution

It introduces a generalized Boolean model with M-estimation, extending previous maximum likelihood approaches for better data fitting.

Findings

Generalized model fits experimental data better.

M-estimators provide robust parameter estimates.

Estimator of total flow accounts for particle clumps.

Abstract

Probability models are proposed for passage time data collected in experiments with a device 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 fit in these experiments. An estimator of total particle flow is constructed by conditioning on lengths of multi-particle clumps.