𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Remarks on compound Poisson approximation of Gaussian random sequences

✍ Scribed by Enkelejd Hashorva; Jürg Hüsler

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
117 KB
Volume
57
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

Let {X i ; i ¿ 1} be a sequence of m-dependent stationary standard Gaussian random variables and u n ; n ∈ N some positive constants. In this note we generalise results of Raab (Extremes 1(3) (1999) 29.), who considered compound Poisson approximation for W n = n i=1 1{X i ¿ u n } the number of exceedances above the level u n . More precisely, the main result concerns an upper asymptotic bound for the total variational distance d TV (W n ; CP( * )) where CP( * ) d = N 1 + 2N 2 + • • • + rN r ; with 2 6 r 6 2m and N i d = Poi( i ); i ¿ 0 are independent Poisson random variables.

📜 SIMILAR VOLUMES

On compound Poisson approximation for su
On compound Poisson approximation for sums of random variables
✍ P. Vellaisamy; B. Chaudhuri 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 424 KB

An upper bound for the total variation distance between the distribution of the sum of a sequence of r.v.'s and that of a compound Poisson is derived. Its applications to a general independent sequence and Markov-binomial sequence are demonstrated. (~

On the accuracy of multivariate compound
On the accuracy of multivariate compound Poisson approximation
✍ S.Y. Novak 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 148 KB

We present multivariate generalizations of some classical results on the accuracy of Poisson approximation for the distribution of a sum of 0 -1 random variables. A multivariate generalization of Bradley's theorem (Michigan Math. J. 30 (1983) 69) is established as well.