On the distance between the distributions of random sums
2003 ◽
Vol 40
(01)
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pp. 87-106
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Keyword(s):
In this paper, we consider the total variation distance between the distributions of two random sums S M and S N with different random summation indices M and N. We derive upper bounds, some of which are sharp. Further, bounds with so-called magic factors are possible. Better results are possible when M and N are stochastically or stop-loss ordered. It turns out that the solution of this approximation problem strongly depends on how many of the first moments of M and N coincide. As approximations, we therefore choose suitable finite signed measures, which coincide with the distribution of the approximating random sum S N if M and N have the same first moments.
2003 ◽
Vol 40
(1)
◽
pp. 87-106
◽
Keyword(s):
Keyword(s):
2003 ◽
Vol 40
(02)
◽
pp. 376-390
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1999 ◽
Vol 36
(01)
◽
pp. 97-104
◽
1996 ◽
Vol 33
(01)
◽
pp. 127-137
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Keyword(s):
2003 ◽
Vol 40
(2)
◽
pp. 376-390
◽
1999 ◽
Vol 36
(1)
◽
pp. 97-104
◽
Keyword(s):
Keyword(s):
2017 ◽
Vol 2017
◽
pp. 1-11
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