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Short Communications

Approximation of a generalized binomial distribution

S. Ya. Šorgin

Moscow

Abstract: The distribution of
\begin{gather*} S_n=X_1+\dots+X_n \\ (\mathbf P\{X_j=1\}=p_j,\quad\mathbf P\{X_j=0\}=1-p_j) \end{gather*}
is investigated. Some results are obtained concerning the rate of its convergence to a Poisson law and to some modifications of the Poisson law.

Received: 14.07.1976

 English version: Theory of Probability and its Applications, 1978, 22:4, 846–850

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