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Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous...

On entropies for random partitions of the unit segment

Milena Bieniek, Dominik Szynal (2008)

Kybernetika

We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.

On Functional of Order Statistics.

W. Sendler (1982)

Metrika

On generalized extreme-value order statistics and moments

Shola Adeyemi (2004)

Kragujevac Journal of Mathematics

On Measures of Uniformly Distributed Sequences and Benford's Law.

Peter Schatte (1989)

Monatshefte für Mathematik

On order statistics for random sample size having compound binomial and Poisson distributions

Zofia Grudzień, D. Szynal (1982)

Applicationes Mathematicae

On the approximation of an integral by a sum of random variables.

Einmahl, John H.J., Van Zuijlen, Martien C.A. (1998)

Journal of Applied Mathematics and Stochastic Analysis

On the convergence of extreme distributions under power normalization

E. M. Nigm (2008)

Applicationes Mathematicae

This paper deals with the convergence in distribution of the maximum of n independent and identically distributed random variables under power normalization. We measure the difference between the actual and asymptotic distributions in terms of the double-log scale. The error committed when replacing the actual distribution of the maximum under power normalization by its asymptotic distribution is studied, assuming that the cumulative distribution function of the random variables is known. Finally,...

On the distance between the empirical process and its concave majorant in a monotone regression framework

Cécile Durot, Anne-Sophie Tocquet (2003)

Annales de l'I.H.P. Probabilités et statistiques

On the distributions of $L_{p}$ norms of weighted quantile processes

Miklós Csörgö, Lajos Horváth (1990)

Annales de l'I.H.P. Probabilités et statistiques

On the distributions of $R_{m n}^{+} (j)$ and $(D_{m n}^{+}, R_{m n}^{+} (j))$

Jagdish Saran, Kanwar Sen (1982)

Aplikace matematiky

The contents of the paper is concerned with the two-sample problem where $F_{m} (x)$ and $G_{n} (x)$ are two empirical distribution functions. The difference $F_{m} (x) - G_{n} (x)$ changes only at an $x_{i}, i = 1, 2, ..., m + n$ , corresponding to one of the observations. Let $R_{m n}^{+} (j)$ denote the subscript $i$ for which $F_{m} (x_{i}) - G_{n} (x_{i})$ achieves its maximum value $D_{m n}^{+}$ for the $j$ th time $(j = 1, 2, ...)$ . The paper deals with the probabilities for $R_{m n}^{+} (j)$ and for the vector $(D_{m n}^{+}, R_{m n}^{+} (j))$ under $H_{0} : F = G$ , thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model.

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On bounds for the asymptotic power and on Pitman efficiencies of the Cramer-von Mises test

On bounds of the range of ordered variates II.

On Characterizing Distributions by Conditional Expectations of Functions of Order Statistics.

On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals

On Distances and Goodness-of-Fit Tests for Detecting Multimodal Distributions.

On distributions of order statistics for absolutely continuous copulas with applications to reliability