scholarly journals Compound Poisson Approximations for Sums of Random Variables

1986 ◽  
Vol 14 (4) ◽  
pp. 1391-1398 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Random Variables ◽  
Compound Poisson ◽  
Sums Of Random Variables ◽  
Poisson Approximations

Poisson and compound Poisson approximations for random sums of random variables

1996 ◽  
Vol 33 (01) ◽  
pp. 127-137 ◽  
Author(s):  
P. Vellaisamy ◽  
B. Chaudhuri
Keyword(s):  
Lower Bound ◽  
Total Variation ◽  
Random Variables ◽  
Upper Bounds ◽  
Random Sums ◽  
Compound Poisson ◽  
Sums Of Random Variables ◽  
Variation Distance ◽  
Poisson Approximations ◽  
Better Than

We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.

Poisson and compound Poisson approximations for random sums of random variables

1996 ◽  
Vol 33 (1) ◽  
pp. 127-137 ◽  
Author(s):  
P. Vellaisamy ◽  
B. Chaudhuri
Keyword(s):  
Lower Bound ◽  
Total Variation ◽  
Random Variables ◽  
Upper Bounds ◽  
Random Sums ◽  
Compound Poisson ◽  
Sums Of Random Variables ◽  
Variation Distance ◽  
Poisson Approximations ◽  
Better Than

We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.

Compound poisson approximations for sums of 1-dependent random variables. II

2011 ◽  
Vol 51 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Jūratė Petrauskienė ◽  
Vydas Čekanavičius
Keyword(s):  
Random Variables ◽  
Dependent Random Variables ◽  
Compound Poisson ◽  
Poisson Approximations

Compound Poisson approximations for sums of discrete nonlattice variables

2003 ◽  
Vol 35 (1) ◽  
pp. 228-250 ◽  
Author(s):  
V. Čekanavičius ◽  
Y. H. Wang
Keyword(s):  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Set Of Points ◽  
Poisson Measures ◽  
Poisson Approximations

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

Compound Poisson approximations for sums of discrete nonlattice variables

2003 ◽  
Vol 35 (01) ◽  
pp. 228-250 ◽  
Author(s):  
V. Čekanavičius ◽  
Y. H. Wang
Keyword(s):  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Set Of Points ◽  
Poisson Measures ◽  
Poisson Approximations

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

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.

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