The average position of the first maximum in a sample of geometric random variables - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2007

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

Abstract

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.
Fichier principal
Vignette du fichier
dmAH0120.pdf (198.77 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

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

Identifiers

Cite

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⟩

Collections

INSMI TDS-MACS
40 View
396 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More