Poisson Approximation of Bernoulli Point Proceses and Their Superpositions, Via Coupling

A maximal coupling of a Bernoulli point process on an arbitrary compact space by a Poisson process is constructed. Exact computation of the variation distance between the probability laws follows as a consequence. For certain values of the parameters this coupling yields the optimal Poisson approxim...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Karr,Alan F, Serfling,Robert J
Format:	Report
Sprache:	eng
Schlagworte:	APPROXIMATION(MATHEMATICS) Bernoulli point processes COMPUTATIONS COUPLING(INTERACTION) EMBEDDING OPTIMIZATION POINTS(MATHEMATICS) POISSON DENSITY FUNCTIONS POISSON EQUATION PROBABILITY RANDOM VARIABLES RANGE(DISTANCE) Statistics and Probability THEOREMS VARIATIONS YIELD
Online-Zugang:	Volltext bestellen
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	A maximal coupling of a Bernoulli point process on an arbitrary compact space by a Poisson process is constructed. Exact computation of the variation distance between the probability laws follows as a consequence. For certain values of the parameters this coupling yields the optimal Poisson approximation of the given Bernoulli process. A procedure is derived for embedding a triangular array of Bernoulli processes within a single Poisson process; classical Poisson limit theorems are deduced. Keywords: Random variables. (Author)