On some distributions connected with the waiting time in a polynomial scheme

G. I. Ivchenko

Moscow

Abstract: Let, in a polynomial scheme with $N$ equiprobable outcomes, $n$ trials be made, and $\rho_1(n)$ $(\rho_2(n))$ denote the maximum (minimum) sampling frequencies. We consider $(\rho_1(n),\rho_2(n))$ as a random function of time parameter $n$ and study the asymptotic behaviour (as $N\to\infty$) of the random variables $\tau_m=\nu_2(m)-\nu_1(m)$, $\rho_1(\nu_2(m))$ and $\rho_2(\nu_1(m))$, where
$$ \nu_i(m)=\min\{n\colon\rho_i(n)=m\};\quad i=1,2;\quad m\ge1. $$


Received: 13.03.1974

 English version: Theory of Probability and its Applications, 1976, 20:3, 545–559

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