scholarly journals Analisis Risiko Kecelakaan Lalu Lintas di Jalan Raya Kabupaten Nganjuk Menggunakan Poisson Point Process on a Linear Network

Inferensi ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 99
Author(s):  
Nurul Kholisatin ◽  
Achmad Choiruddin
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Linear Network

scholarly journals On Laslett's transform for the Boolean model

2001 ◽  
Vol 33 (1) ◽  
pp. 1-5 ◽  
Author(s):  
A. D. Barbour ◽  
V. Schmidt
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Simple Proof ◽  
Poisson Point Process ◽  
Boolean Model ◽  
Random Sets ◽  
Convex Compact ◽  
Homogeneous Poisson Process ◽  
Vertical Strip ◽  
Cumulative Process

Consider the Boolean model in ℝ2, where the germs form a homogeneous Poisson point process with intensity λ and the grains are convex compact random sets. It is known (see, e.g., Cressie (1993, Section 9.5.3)) that Laslett's rule transforms the exposed tangent points of the Boolean model into a homogeneous Poisson process with the same intensity. In the present paper, we give a simple proof of this result, which is based on a martingale argument. We also consider the cumulative process of uncovered area in a vertical strip and show that a (linear) Poisson process with intensity λ can be embedded in it.

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