Radial generation of n-dimensional poisson processes

1984 ◽  
Vol 21 (03) ◽  
pp. 548-557
Author(s):  
M. P. Quine ◽  
D. F. Watson
Keyword(s):  
Poisson Process ◽  
Poisson Processes ◽  
Three Dimensions ◽  
Simulation Studies ◽  
Simple Method ◽  
Efficient Simulation ◽  
Nearest Neighbours

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in ann-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

Radial generation of n-dimensional poisson processes

1984 ◽  
Vol 21 (3) ◽  
pp. 548-557 ◽  
Author(s):  
M. P. Quine ◽  
D. F. Watson
Keyword(s):  
Poisson Process ◽  
Poisson Processes ◽  
Three Dimensions ◽  
Simulation Studies ◽  
Simple Method ◽  
Efficient Simulation ◽  
Nearest Neighbours

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in an n-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

A new graph related to the directions of nearest neighbours in a point process

2003 ◽  
Vol 35 (1) ◽  
pp. 47-55 ◽  
Author(s):  
S. N. Chiu ◽  
I. S. Molchanov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Point Process ◽  
Process Simulation ◽  
Point Processes ◽  
Nearest Neighbour ◽  
Simulation Studies ◽  
Nearest Neighbours ◽  
Typical Point

This paper introduces a new graph constructed from a point process. The idea is to connect a point with its nearest neighbour, then to the second nearest and continue this process until the point belongs to the interior of the convex hull of these nearest neighbours. The number of such neighbours is called the degree of a point. We derive the distribution of the degree of the typical point in a Poisson process, prove a central limit theorem for the sum of degrees, and propose an edge-corrected estimator of the distribution of the degree that is unbiased for a stationary Poisson process. Simulation studies show that this degree is a useful concept that allows the separation of clustering and repulsive behaviour of point processes.

A new graph related to the directions of nearest neighbours in a point process

2003 ◽  
Vol 35 (01) ◽  
pp. 47-55
Author(s):  
S. N. Chiu ◽  
I. S. Molchanov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Point Process ◽  
Process Simulation ◽  
Point Processes ◽  
Nearest Neighbour ◽  
Simulation Studies ◽  
Nearest Neighbours ◽  
Typical Point

This paper introduces a new graph constructed from a point process. The idea is to connect a point with its nearest neighbour, then to the second nearest and continue this process until the point belongs to the interior of the convex hull of these nearest neighbours. The number of such neighbours is called the degree of a point. We derive the distribution of the degree of the typical point in a Poisson process, prove a central limit theorem for the sum of degrees, and propose an edge-corrected estimator of the distribution of the degree that is unbiased for a stationary Poisson process. Simulation studies show that this degree is a useful concept that allows the separation of clustering and repulsive behaviour of point processes.

On some characterizations of the poisson process

1989 ◽  
Vol 26 (01) ◽  
pp. 176-181
Author(s):  
Wen-Jang Huang
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Arrival Time ◽  
Random Variables ◽  
Poisson Processes

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.

Convergence to equilibrium in a traffic model with restricted passing

1979 ◽  
Vol 16 (4) ◽  
pp. 881-889 ◽  
Author(s):  
Hans Dieter Unkelbach
Keyword(s):  
Poisson Process ◽  
Limit Theorems ◽  
Point Processes ◽  
Road Traffic ◽  
Poisson Processes ◽  
Traffic Model ◽  
Cluster Point ◽  
Convergence To Equilibrium ◽  
Constant Intensity

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes.The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

scholarly journals Intersection densities of nonstationary Poisson processes of hypersurfaces

2007 ◽  
Vol 39 (2) ◽  
pp. 307-317 ◽  
Author(s):  
Lars Michael Hoffmann
Keyword(s):  
Poisson Process ◽  
Large Class ◽  
Poisson Processes

Intersection densities are introduced for a large class of nonstationary Poisson processes of hypersurfaces and inequalities for them are proved. In doing so, similar results from both Wieacker (1986) and Schneider (2003) are summarized in one theorem and the concept of an associated zonoid of a Poisson process of hypersurfaces is generalized to a nonstationary setting.

scholarly journals Direct fast estimator for recombination frequency in the F2 cross

2021 ◽  
Author(s):  
Mathias Lorieux
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Maximum Likelihood Estimator ◽  
Recombination Frequency ◽  
Short Note ◽  
Simulation Studies ◽  
Likelihood Estimator ◽  
Simple Estimate ◽  
Efficient Simulation

AbstractIn this short note, a new unbiased maximum-likelihood estimator is proposed for the recombination frequency in the F2 cross. The estimator is much faster to calculate than its EM algorithm equivalent, yet as efficient. Simulation studies are carried to illustrate the gain over another simple estimate proposed by Benito & Gallego (2004).

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

BLOCKCHAIN DOUBLE-SPEND ATTACK DURATION

2020 ◽  
pp. 1-9
Author(s):  
Mark Brown ◽  
Erol Peköz ◽  
Sheldon Ross
Keyword(s):  
Poisson Process ◽  
Closed Form ◽  
Exact Expression ◽  
Computational Power ◽  
Efficient Simulation ◽  
Analytic Approximations

Many cryptocurrencies including Bitcoin are susceptible to a so-called double-spend attack, where someone dishonestly attempts to reverse a recently confirmed transaction. The duration and likelihood of success of such an attack depends on the recency of the transaction and the computational power of the attacker, and these can be related to the distribution of time for counts from one Poisson process to exceed counts from another by some desired amount. We derive an exact expression for this distribution and show how it can be used to obtain efficient simulation estimators. We also give closed-form analytic approximations and illustrate their accuracy.

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