Displaying similar documents to “On general asymptotic behaviour of order statistics with random index.”

Limit theorems for bivariate extremes of non-identically distributed random variables

H. M. Barakat (2002)

Applicationes Mathematicae

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The limit behaviour of the extreme order statistics arising from n two-dimensional independent and non-identically distributed random vectors is investigated. Necessary and sufficient conditions for the weak convergence of the distribution function (d.f.) of the vector of extremes, as well as the form of the limit d.f.'s, are obtained. Moreover, conditions for the components of the vector of extremes to be asymptotically independent are studied.

Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ( S n ) n 0 be a -random walk and ( ξ x ) x be a sequence of independent and identically distributed -valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on 2 with values in . We study the weak convergence of the sequence 𝒰 n , n , with values in D [ 0 , 1 ] the set of right continuous real-valued functions with left limits, defined by i , j = 0 [ n t ] h ( ξ S i , ξ S j ) , t [ 0 , 1 ] . Statistical applications are presented, in particular we prove a strong law of large numbers for...

On Dwass' method for deriving the distribution of rank order statistics

B. R. Handa, Sri Gopal Mohanty (1979)

Aplikace matematiky

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This note presents a critical examination of Dwass' method for obtaining the distribution of rank order statistics defined on random samples obtained from the same continuous population. New situations are discussed for the usefulness of the method.