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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2007

The average position of the first maximum in a sample of geometric random variables

Résumé

We consider samples of n geometric random variables $(Γ _1, Γ _2, \dots Γ _n)$ where $\mathbb{P}\{Γ _j=i\}=pq^{i-1}$, for $1≤j ≤n$, with $p+q=1$. The parameter we study is the position of the first occurrence of the maximum value in a such a sample. We derive a probability generating function for this position with which we compute the first two (factorial) moments. The asymptotic technique known as Rice's method then yields the main terms as well as the Fourier expansions of the fluctuating functions arising in the expected value and the variance.
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Dates et versions

hal-01184771 , version 1 (17-08-2015)

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Margaret Archibald, Arnold Knopfmacher. The average position of the first maximum in a sample of geometric random variables. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.295-306, ⟨10.46298/dmtcs.3523⟩. ⟨hal-01184771⟩

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