On compound Poisson approximation for sums of random variables

1999 ◽  
Vol 41 (2) ◽  
pp. 179-189 ◽  
Author(s):  
P. Vellaisamy ◽  
B. Chaudhuri
Keyword(s):  
Random Variables ◽  
Poisson Approximation ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
Sums Of Random Variables

scholarly journals Compound Poisson Approximation for Dissociated Random Variables via Stein's Method

1999 ◽  
Vol 8 (4) ◽  
pp. 335-346 ◽  
Author(s):  
PETER EICHELSBACHER ◽  
MAŁGORZATA ROOS
Keyword(s):  
System Reliability ◽  
Random Variables ◽  
Poisson Approximation ◽  
Stein’S Method ◽  
Stein's Method ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
Stein Equation

In the present paper we consider compound Poisson approximation by Stein's method for dissociated random variables. We present some applications to problems in system reliability. In particular, our examples have the structure of an incomplete U-statistics. We mainly apply techniques from Barbour and Utev, who gave new bounds for the solutions of the Stein equation in compound Poisson approximation in two recent papers.

scholarly journals Between Individual and Collective Model for the Total Claims

1988 ◽  
Vol 18 (2) ◽  
pp. 169-174 ◽  
Author(s):  
R. Kaas ◽  
A. E. van Heerwaarden ◽  
M. J. Goovaerts
Keyword(s):  
Life Insurance ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Collective Model ◽  
Individual Model ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
The Real ◽  
Stop Loss

AbstractThis article studies random variables whose stop-loss rank falls between a certain risk (assumed to be integer-valued and non-negative, but not necessarily of life-insurance type) and the compound Poisson approximation to this risk. They consist of a compound Poisson part to which some independent Bernoulli-type variables are added.Replacing each term in an individual model with such a random variable leads to an approximating model for the total claims on a portfolio of contracts that is computationally almost as attractive as the compound Poisson approximation used in the standard collective model. The resulting stop-loss premiums are much closer to the real values.

scholarly journals Compound Poisson approximation for the distribution of extremes

2002 ◽  
Vol 34 (1) ◽  
pp. 223-240 ◽  
Author(s):  
A. D. Barbour ◽  
S. Y. Novak ◽  
A. Xia
Keyword(s):  
Point Processes ◽  
Poisson Approximation ◽  
Value Theory ◽  
Wasserstein Metric ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
Limiting Behaviour ◽  
Explicit Bounds ◽  
Empirical Point ◽  
Poisson Cluster

Empirical point processes of exceedances play an important role in extreme value theory, and their limiting behaviour has been extensively studied. Here, we provide explicit bounds on the accuracy of approximating an exceedance process by a compound Poisson or Poisson cluster process, in terms of a Wasserstein metric that is generally more suitable for the purpose than the total variation metric. The bounds only involve properties of the finite, empirical sequence that is under consideration, and not of any limiting process. The argument uses Bernstein blocks and Lindeberg's method of compositions.

Sign in / Sign up

Export Citation Format

Share Document