Abstract
The almost certain (probability one) behavior of row sums
of double arrays of rowwise independent random variables Xn, i is investigated primarily when the Xn, i assume only the values zero and one. If knpn, the expected number of successes, grows more rapidly than C log n, then
converges almost certainly to one. However, when the expected number of successes grows less rapidly than C log n, it no longer determines the asymptotic behavior of
and the outcome depends upon additional stochastic assumptions. Two alternative sets of stochastic constraints are imposed and the behavior of
under each is analyzed and contrasted. Finally, the case of exponential random variables is considered briefly.
Keywords
- Triangular Array
- Independent Column
- Poisson Probability
- Standard Normal Density
- Poisson Case
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Research supported by the National Science Foundation under Grant NSF-MCS-8005481.
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© 1981 Springer-Verlag
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Teicher, H. (1981). Almost certain behavior of row sums of double arrays. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097322
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DOI: https://doi.org/10.1007/BFb0097322
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