Propagation Models and Fitting Them for the Boolean Random Sets

Subject Areas : Design of Experiment

mojtaba Khazaei ¹ , Khalil Shafie ²

1 - Assistant Professor, Department of Statistics, Shahid Beheshti University G.C., Tehran, IRAN.
2 - Associate Professor, University of Northern Colorado, Colorado, USA.

Received: 2008-03-08 Accepted : 2009-03-22 Published : 2010-02-07

Keywords: random closed set, hitting functional, Poisson point process, Boolean model, lower positive tangent points,

Abstract :

In order to study the relationship between random Boolean sets and some explanatory variables, this paper introduces a Propagation model. This model can be applied when corresponding Poisson process of the Boolean model is related to explanatory variables and the random grains are not affected by these variables. An approximation for the likelihood is used to find pseudo-maximum likelihood estimates of propagation model parameters when the grains are nonrandom circle with unknown radii.