We derive exact and asymptotic formulas for the probability that a symmetric n×n matrix with unit diagonal and upper diagonal elements i.i.d. uniform on (−1,1) is positive definite (and thus a ...“random correlation matrix”): this is almost never the case for n≥6.
We consider the problem of testing whether r 2 samples are drawn from the same continuous distribution F(x). The test statistic we will study in some detail is defined as the maximum of the circular ...differences of the empirical distribution functions, a generalization of the classical 2-sample Kolmogorov-Smirnov test to r 2 independent samples. For the case of equal sample sizes we derive the exact null distribution by counting lattice paths confined to stay in the scaled alcove ${\cal A}$r of the affine Weyl group Ar1. This is done using a generalization of the classical reflection principle. By a standard diffusion scaling we derive also the asymptotic distribution of the test statistic in terms of a multivariate Dirichlet series. When the sample sizes are not equal the reflection principle no longer works, but we are able to establish a weak convergence result even in this case showing that by a proper rescaling a test statistic based on a linear transformation of the circular differences of the empirical distribution functions has the same asymptotic distribution as the test statistic in the case of equal sample sizes.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this paper we consider an analogue of the classical simple random walk on the set of integers which has correlated increments. In particular we are interested in the distribution of the absorption ...times and the maximum of such processes. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
We discuss queueing systems subject to total disasters. If the time intervals between successive disasters are i.i.d. random variables independent of arrival and service process and arrivals form a ...Poisson process, then the transient and the asymptotic analysis of such models may be based on Feller's Second Renewal Theorem. Several examples are given: the limiting behavior of M/G/1 in case of exponential disasters and its special cases M/M/1, M/M/1/K and M/M/infinity. (author´s abstract)
Series: Research Report Series / Department of Statistics and Mathematics
We consider an M/G/1 queueing model with N-policy operating. This means, that the server will start up only if a queue of a prescribed length has built up. For this model the time dependent ...distribution of the queue lenght is given by simple renewal arguments without resorting to integral transform techniques. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
The transition fundions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's Theorem for counting ...lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
Die analytische Herleitung der Wahrscheinlichkeitsdichte der Busy Period in Warteschlangenmodellen mit exponentiellen Service- und Erlang verteilten Zwischenankunftszeiten ist mit beträchtlichem ...Aufwand verbunden. Eine vergleichsweise elementare Lösung wird möglich durch Anwendung von Methoden der Gitterpfadkombinatorik. (Autorenref.)
Series: Forschungsberichte / Institut für Statistik
