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The convergence to normal distribution of random sums of independent random variables with finite variances

Let (Xnk) be a double sequence of random variables with finite variances. Let (Zn) be a sequence of positive integral-valued random variables such that for each n, Zn, Xn1, Xn2,... are independent and Unk = 0, where Unk is the expectation of Xnk.
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Integro-Local and Local Theorems on Normal and Large Deviations of the Sums of Nonidentically Distributed Random Variables in the Triangular Array Scheme

Theory of Probability & Its Applications, 2010
Gnedenko's local theorem and Stone–Shepp's integro-local theorem (see [L. A. Shepp, Ann. Math. Statist., 35 (1964), pp. 419–423], [C. Stone, Ann. Math. Statist., 36 (1965), pp. 546–551], [B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA, 1954]) for sums on independent ...
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The static stochastic knapsack problem with normally distributed item sizes

Mathematical programming, 2011
Yasemin Merzifonluoglu   +2 more
semanticscholar   +1 more source

Multiple comparisons and sums of dissociated random variables

Advances in Applied Probability, 1985
A. Barbour, G. Eagleson
semanticscholar   +1 more source

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