Zobrazeno 1 - 10 of 10 pro vyhledávání: '"Anatole Joffe"'
1
On Sums of Products of Bernoulli Variables and Random Permutations
Autor: François Perron, Anatole Joffe, Paul Popadiuk, Eric Marchand
Publikováno v: Journal of Theoretical Probability. 17:285-292
Let {X k } k≥1 be independent Bernoulli random variables with parameters p k . We study the distribution of the number or runs of length 2: that is $$S_n = \sum {_{k = 1}^n {\text{ }}X_k X_{k + 1}}$$ . Let S=lim n→∞ S n . For the particular cas
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::03c6c93d00de26f173316374b1c9ff77
https://doi.org/10.1023/b:jotp.0000020485.34082.8c
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2
Expectation of the Ratio of the Sum of Squares to the Square of the Sum: Exact and Asymptotic Results
Autor: Józef L Teugels, Aimé Fuchs, Anatole Joffe
Publikováno v: Theory of Probability & Its Applications. 46:243-255
Let $X_i$, $i=1,\ldots,n$, be a sequence of positive independent identically distributed random variables. Define $$ R_n : = {\bf E} \frac{X_1^2 + X_2^2 + \cdots + X_n^2} {(X_1 + X_2 + \cdots + X_n)^2}. $$ Let $\varphi(s) = {\bf E} e^{-sX}$. We give
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b9d4d17aba22351f906cb3acaae74ff5
https://doi.org/10.1137/s0040585x97978919
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4
Formule exacte de l'espérance du rapport de la somme des carrés par le carré de la somme
Autor: Anatole Joffe, Aimé Fuchs
Publikováno v: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. 325:907-909
Let (Xn)(n ≥ 1) be a sequence of identically distributed independent nonnegative random variables satisfying P {X1 = 0} < 1. The asymptotic behaviour of the ratio Rn = E'[(X12 + … + Xn2)/(X1 + … + Xn)2] has been studied by McLeish and O'Brien.
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ebabb6be39e1774ea30fd5da35892402
https://doi.org/10.1016/s0764-4442(97)80136-x
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6
Un modele probabiliste utile en biologie moleculaire
Autor: Anatole Joffe
Publikováno v: Journal of Applied Probability. 19:660-663
Let X 1 ··· Xn be i.i.d.r.v.'s uniformly distributed on [0, l]. Let X (1) ··· X (n) be the ordered r.v.'s 0≦ X (1) ≦ X (2)···≦ X (n) ≦ l. We obtain the n + 1 intervals (X (i), X (i+1)) n i=0, with X (0) = 0, X (n+1)= l of length Li =
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6c8192599fad849b11330bce5f91dbe0
https://doi.org/10.1017/s0021900200037141
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