Poisson and compound Poisson approximations for random sums of random variables
1996 ◽
Vol 33
(01)
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pp. 127-137
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Keyword(s):
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.
Keyword(s):
2003 ◽
Vol 40
(01)
◽
pp. 87-106
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Keyword(s):
1983 ◽
Vol 15
(03)
◽
pp. 585-600
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2003 ◽
Vol 40
(1)
◽
pp. 87-106
◽
Keyword(s):
1986 ◽
Vol 14
(4)
◽
pp. 1391-1398
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Keyword(s):
2002 ◽
Vol 34
(03)
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pp. 609-625
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