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Monotonicity and Aging Properties of Random Sums
"... In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions the distribution of a Poisson sum is PF2 by approximating a Poisson sum by a sequence of binomial sums. The ..."
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Cited by 4 (0 self)
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In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions the distribution of a Poisson sum is PF2 by approximating a Poisson sum by a sequence of binomial sums
Stochastic comparison of multivariate random sums
, 2004
"... Key words and phrases: multivariate random sums, multivariate stochastic orders, convex order, directionally convex order, supermodular function We establish preservation results for the stochastic comparison of multivariate random sums of stationary, not necessary independent, sequences of nonnegat ..."
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Key words and phrases: multivariate random sums, multivariate stochastic orders, convex order, directionally convex order, supermodular function We establish preservation results for the stochastic comparison of multivariate random sums of stationary, not necessary independent, sequences
Normal approximation for random sums
, 2006
"... In this paper, we adapt the very effective Berry–Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point pr ..."
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Cited by 10 (5 self)
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In this paper, we adapt the very effective Berry–Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point
PROBABILITY INEQUALITIES FOR SUMS OF BOUNDED RANDOM VARIABLES
, 1962
"... Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the s ..."
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Cited by 2215 (2 self)
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Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1791 (69 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Bounds of the normal approximation to randomsum
, 2014
"... ABSTRACT: Consider sequences {Xi}∞i=1 and {Yj}∞j=1 of independent and identically distributed (i.i.d.) random variables, random variables K1, K2 ranging over of all positive integers, where the Xi’s, Yj’s, K1, and K2 are all independent. We obtain BerryEsseen bounds for randomsum Wilcoxon’s statis ..."
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ABSTRACT: Consider sequences {Xi}∞i=1 and {Yj}∞j=1 of independent and identically distributed (i.i.d.) random variables, random variables K1, K2 ranging over of all positive integers, where the Xi’s, Yj’s, K1, and K2 are all independent. We obtain BerryEsseen bounds for randomsum Wilcoxon’s
1 Exponential Bounds for Random Sums.
, 2004
"... Abstract. We construct a non improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand. ..."
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Abstract. We construct a non improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.
Almost odd random sumfree sets
, 2008
"... We show that if S1 is a strongly complete sumfree set of positive integers, and if S0 is a finite sumfree set, then with positive probability a random sumfree set U contains S0 and is contained in S0 âª S1. As a corollary we show that with positive probability, 2 is the only even element of a ra ..."
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Cited by 2 (1 self)
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We show that if S1 is a strongly complete sumfree set of positive integers, and if S0 is a finite sumfree set, then with positive probability a random sumfree set U contains S0 and is contained in S0 âª S1. As a corollary we show that with positive probability, 2 is the only even element of a
Multinomial Latent Model for Random Sums
"... probability generating function. Abstract. Let us consider a collective insurance contract in some fixed time period (0, T]. Let N denote the number of claims in (0, T] and Y1, Y2,... YN the corresponding claims. Then SN = ∑N i=1 Yi is the total claim amount. In the classical theory it is assumed t ..."
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that (i) N and (Y1, Y2,...) are independent random variables (r.v.’s); (ii) Y1, Y2,... are independent and (iii) Y1, Y2,... have the same distribution. In this paper we relax the condition (ii) supposing that the claim amounts are dependent random variables. Our analysis is based on the correlation
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