Statistics and Data Science Seminar
Dr. Grace L. Yang
DMS/NSF & Department of Mathematics, University of Maryland, College Park
Correction for interarrival time distribution in the Estimation of Poisson Intensity
Abstract: Occurrence of dead time in recording instruments poses challenging problems in
data acquisition, construction of stochastic models and statistical analysis.
Well-known examples include the construction of probability models for a
paralyzable counter (electron multiplier) and a nonparalyzable counter (e.g.,
Geiger counter). In this presentation, statistical analysis of recordings from
Phase Doppler Interferometry (PDI)is considered. PDI is a non-intrusive
technique used to obtain information about spray characteristics in many
areas of science, such as liquid fuel spray in combustion, spray coatings, fire
suppression and pesticide dispensing. PDI can record the velocity of individual
droplets in a spray. However, it will miss some of the droplets because of a
recurring presence of dead time. The incompleteness of PDI recordings results in
a multimodal interarrival time distribution of droplets. Modeling a spray
process as a homogeneous Poisson process, we estimate the spray diffusion rate
(Poisson intensity) with correction for dead time under various conditions. The
asympotic distribution of the estimates is derived from a strict stationary
process. Simulation produced a good agreement between our estimators (in the
presence of dead time) and the MLE obtained without dead time. Experimental data
from NIST are used for illustration.
Wednesday October 25, 2006 at 3:30 PM in SEO 512