Smoothing effect of compound Poisson approximations to the distributions of weighted sums

2014 ◽  
Vol 54 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Vydas Čekanavičius ◽  
Aistė Elijio
Keyword(s):  
Weighted Sums ◽  
Smoothing Effect ◽  
Compound Poisson ◽  
Poisson Approximations

Asymptotic Expansions in the Exponent: a Compound Poisson Approach

1997 ◽  
Vol 29 (02) ◽  
pp. 374-387 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansion ◽  
Large Deviations ◽  
Poisson Distribution ◽  
Asymptotic Expansions ◽  
Compound Poisson ◽  
Poisson Measures ◽  
Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

Compound Poisson approximations for word patterns under Markovian hypotheses

1995 ◽  
Vol 32 (04) ◽  
pp. 877-892 ◽  
Author(s):  
Mark X. Geske ◽  
Anant P. Godbole ◽  
Andrew A. Schaffner ◽  
Allison M. Skolnick ◽  
Garrick L. Wallstrom
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Compound Poisson ◽  
Letter Word ◽  
Stationary Markov Chain ◽  
Letter Alphabet ◽  
Poisson Approximations

Consider a stationary Markov chainwith state space consisting of theξ-letter alphabet set Λ= {a1, a2, ···,aξ}.We study the variablesM=M(n, k) andN=N(n, k),defined, respectively, as the number of overlapping and non-overlapping occurrences of a fixed periodick-letter word, and use the Stein–Chen method to obtain compound Poisson approximations for their distribution.

scholarly journals Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary markov chain

2007 ◽  
Vol 39 (01) ◽  
pp. 128-140 ◽  
Author(s):  
Etienne Roquain ◽  
Sophie Schbath
Keyword(s):  
Markov Chain ◽  
Poisson Distribution ◽  
Approximation Error ◽  
Rare Event ◽  
Poisson Approximation ◽  
Rare Word ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
Stein Method ◽  
Poisson Approximations

We derive a new compound Poisson distribution with explicit parameters to approximate the number of overlapping occurrences of any set of words in a Markovian sequence. Using the Chen-Stein method, we provide a bound for the approximation error. This error converges to 0 under the rare event condition, even for overlapping families, which improves previous results. As a consequence, we also propose Poisson approximations for the declumped count and the number of competing renewals.

Compound poisson approximations for the numbers of extreme spacings

1993 ◽  
Vol 25 (04) ◽  
pp. 847-874 ◽  
Author(s):  
Małgorzata Roos
Keyword(s):  
Poisson Approximation ◽  
Expected Number ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Poisson Approximations ◽  
Better Than

The accuracy of the Poisson approximation to the distribution of the numbers of large and small m-spacings, when n points are placed at random on the circle, was analysed using the Stein–Chen method in Barbour et al. (1992b). The Poisson approximation for m≧2 was found not to be as good as for 1-spacings. In this paper, rates of approximation of these distributions to suitable compound Poisson distributions are worked out, using the CP–Stein–Chen method and an appropriate coupling argument. The rates are better than for Poisson approximation for m≧2, and are of order O((log n)2/n) for large m-spacings and of order O(1/n) for small m-spacings, for any fixed m≧2, if the expected number of spacings is held constant as n → ∞.

Poisson approximations for the distribution and moments of ordered m-spacings

1994 ◽  
Vol 31 (A) ◽  
pp. 271-281 ◽  
Author(s):  
Joseph Glaz ◽  
Joseph Naus ◽  
Malgorzata Roos ◽  
Sylvan Wallenstein
Keyword(s):  
Simulation Study ◽  
Numerical Procedure ◽  
Poisson Approximation ◽  
Accurate Approximation ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
Poisson Approximations

This article investigates the accuracy of approximations for the distribution of ordered m-spacings for i.i.d. uniform observations in the interval (0, 1). Several Poisson approximations and a compound Poisson approximation are studied. The result of a simulation study is included to assess the accuracy of these approximations. A numerical procedure for evaluating the moments of the ordered m-spacings is developed and evaluated for the most accurate approximation.

Sign in / Sign up

Export Citation Format

Share Document