Geodesic
On some distributions connected with the waiting time in a~polynomial scheme
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 557-570

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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 $$ \nu_i(m)=\min\{n\colon\rho_i(n)=m\};\quad i=1,2;\quad m\ge1. $$ 
@article{TVP_1975_20_3_a5,
     author = {G. I. Ivchenko},
     title = {On some distributions connected with the waiting time in a~polynomial scheme},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {557--570},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a5/}
}
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G. I. Ivchenko. On some distributions connected with the waiting time in a~polynomial scheme. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 557-570. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a5/