Consistent Estimation of Poisson Intensity in the Presence of Dead Time
S X. He, Grace L. Yang, K T. fang, J F. Widmann
Phase Doppler Interferometry (PDI) is a non-intrusive technique frequently used to obtain information about spray characteristics. Understanding spray characteristics is of critical importance in many areas of science, including liquid fuel spray combustion, spray coatings, fire suppression, and pesticides. PDI measures the size and velocity of individual droplets in the spray. Due to the design of the instrument, the recordings of the PDI contain gaps, called dead times. The presence of the recurrent dead times greatly complicates the estimation of the diffusion rate of the droplets. Modeling the spray process as a homogeneous Poisson process, we construct consistent estimators of the diffusion rate (Poisson intensity) under various conditions. Asymptotic normality of the estimators are discussed. Simulation results indicate good agreement of our estimators (in the presence of dead time) with the MLE obtained without dead time. For illustration, experimental data are used to estimate the Poisson intensity.