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A Complete Proof of Universal Inequalities for the Distribution Function of the Binomial Law
We present a new form and a short complete proof of explicit two-sided estimates for the distribution function $F_{n,p}(k)$ of the binomial law with parameters $n,p$ from [D. Alfers and H. Dinges, Z.Expand
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Controlled Branching Processes
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Branching processes. II
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Inequalities for the distribution of a sum of functions of independent random variables
AbstractLet $$\xi = \sum\nolimits_{i_1 ,...,i_r = 1}^n {f_{i_1 ,...,i_r } (\zeta _{i_1 ,...,} \zeta _{\iota _r } )}$$ where ζ1,..., ζn are independent random variables and the $$f_{i_1 ,...,i_r }$$Expand
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A condition for the extinction of a bounded branching process
A subcritical Galton-Watson process is investigated under the condition that the number of particles is bounded above (“superfluous” particles are annihilated). A necessary and sufficient conditionExpand
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