Poisson approximation for a sum of dependent indicators: an alternative approach
2002 ◽
Vol 34
(3)
◽
pp. 609-625
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Keyword(s):
The random variables X1, X2, …, Xn are said to be totally negatively dependent (TND) if and only if the random variables Xi and ∑j≠iXj are negatively quadrant dependent for all i. Our main result provides, for TND 0-1 indicators X1, x2, …, Xn with P[Xi = 1] = pi = 1 - P[Xi = 0], an upper bound for the total variation distance between ∑ni=1Xi and a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.
2002 ◽
Vol 34
(03)
◽
pp. 609-625
◽
1983 ◽
Vol 15
(03)
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pp. 585-600
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2010 ◽
Vol 47
(3)
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pp. 826-840
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2010 ◽
Vol 47
(03)
◽
pp. 826-840
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1993 ◽
Vol 25
(02)
◽
pp. 334-347
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2004 ◽
Vol 41
(4)
◽
pp. 1081-1092
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2003 ◽
Vol 40
(02)
◽
pp. 376-390
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