- Tytuł:
- On the number of empty cells in the allocation scheme of indistinguishable particles
- Autorzy:
-
Chuprunov, Alexey
Fazekas, Istvan - Powiązania:
- https://bibliotekanauki.pl/articles/1395925.pdf
- Data publikacji:
- 2020
- Wydawca:
- Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
- Tematy:
-
Allocation scheme of indistinguishable particles into different cells
Gaussian random variable
Berry-Esseen inequality
limit theorem
local limit theorem - Opis:
- The allocation scheme of \(n\) indistinguishable particles into \(N\) different cells is studied. Let the random variable \(\mu_0(n,K,N)\) be the number of empty cells among the first \(K\) cells. Let \(p=\frac{n}{n+N}\). It is proved that \(\frac{\mu_0(n,K,N)-K(1-p)}{\sqrt{ K p(1-p)}}\) converges in distribution to the Gaussian distribution with expectation zero and variance one, when \(n,K, N\to\infty\) such that \(\frac{n}{N}\to\infty\) and \(\frac{n}{NK}\to 0\). If \(n,K, N\to\infty\) so that \(\frac{n}{N}\to\infty\) and \(\frac{NK}{n}\to \lambda\), where \(0<\lambda<\infty\), then \(\mu_0(n,K,N)\) converges in distribution to the Poisson distribution with parameter \(\lambda\). Two applications of the results are given to mathematical statistics. First, a method is offered to test the value of \(n\). Then, an analogue of the run-test is suggested with an application in signal processing.
- Źródło:
-
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2020, 74, 1
0365-1029
2083-7402 - Pojawia się w:
- Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
- Dostawca treści:
- Biblioteka Nauki
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