This paper focuses on newmeasures of performance in single-server Markovian queueing system. These measures depend on the moments of order statistics. The expected value and the variance of the maximum minimum number of customers in the system as well as the expected value and the variance of the minimum maximum waiting time are presented. Application to an M/M/1 model is given to illustrate th...

A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict that the distribution will again be a Gaussian, with a specific mean and variance. The variance splits naturally into a bulk and surface contibution, the lat...

In the case of two signals with independent pairs of observations (x n ,y n ) a statistic to estimate the variance of the histogram based mutual information estimator has been derived earlier. We present such a statistic for dependent pairs. To derive this statistic it is necessary to avail of a reliable statistic to estimate the variance of the sample mean in case of dependent observations. We...

The mean and the variance value of a random variable play an important role in statistical analysis. Sometimes the available observations are not precise, and we want to test the hypotheses of mean and variance in such environment. Hence, in this paper, we first extend and introduced L2−metric based on imprecise (fuzzy) observations, and then, the concepts of fuzzy test statistics are defined b...

Many people who do data analysis take only a few classes in statistics and hence, in general, get introduced only to classical methods of statistics; i.e., least squares, normal theory, and possibly maximum likelihood methods. The motivation for most of these techniques is the maximizing of a function of the data with respect to some parameter—mean, variance, slope, e.g. Calculus is used by tak...

Abstract. This paper deals with the problem of testing a change in variance of the p-th order autoregressive process, AR(p), at an unknown change point τ . We propose a test based on maximum likelihood principle for detecting such type of change, find asymptotic distribution of the test statistic and compare it with the tests for detecting changes in both variance and autoregressive parameters ...

The problem of variance estimation for a t ime series with linear trend is studied using model based procedures. The work done by Royall and Cumberland ((2), (3)) is refined and adapted to the special problems of the Current Employment Survey (790 Survey) at the Bureau of Labor Statistics. A variety of variance estimation techniques are examined; including a variation of jackknife estimation an...

We present in this work results on some distributions of permutation statistics of random elements of the wreath product Gr,n = Cr ! Sn. We consider the distribution of the descent number, the flag major index, the excedance, and the number of fixed points, over the whole group Gr,n or over the subclasses of derangements and involutions. We compute the mean, variance and moment generating funct...

This analysis introduces a generalization of the basic statistical concepts of expectation values and variance for non-Euclidean metrics induced by L-norms. The non-Euclidean L means are defined by exploiting the fundamental property of minimizing the L deviations that compose the L variance. These L expectation values embody a generic formal scheme of means characterization. Having the p-norm ...