DOAJ
Open Access
2007
The average position of the first maximum in a sample of geometric random variables
Margaret Archibald
Arnold Knopfmacher
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
M
Margaret Archibald
A
Arnold Knopfmacher
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2007
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.3523
- Akses
- Open Access ✓