Measure Distributions for Some Poisson Process Random Domains and Statistical Applications

Abstract

We define random domains originated by a homogeneous planar Poisson process on that have been never considered before. Distributional results are stated and proved for the Lebesgue measure of the considered domains. Statistical applications are outlined.

Keywords:

• Exponential and gamma distributions
• Natural filtration
• Parametric inference
• Planar Poisson process

Mathematics Subject Classification:

• 60G55
• 60D05