What should it mean for us to say that two distributions are close, or that a sequence μn of distributions of some random variables Xn taking values in some state space X converges to another distribution μ of some random variable X? Certainly we’ll need to know if Xn and X are close, so we’ll restrict ourselves to state spaces X that are sigma-compact metric spaces (and to avoid needless techn...

Let {Xn ,n=>1} be a strictly stationary sequence of negatively associated random variables, with common distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) for fixed $K /in N$ based on kernel type estimators. We introduce asymptotic normality and properties and moments. From these we derive the optimal bandwidth...

In this paper we use Wynn’s -algorithm to accelerate certain numerical sequences, in order to study empirically their rate of convergence, for the sequence of successive approximations associated with some test functions and ordinary differential equations. For the great majority of the test sequences, the -algorithm does not improve the convergence rate. Subject Classification: [2000] 47H10, 6...

A random variable is a measurable function from an uncertainty space to the set of real numbers, which is used to model randomness. An uncertain variable is a measurable function from uncertainty space to the set of real numbers, which is used to describe uncertainty. However, randomness and uncertainty often simultaneously appear in a complex system. Uncertain random variable provides a useful...

Korovkin-type theorems in modular spaces and applications C. Bardaro ∗ A. Boccuto † X. Dimitriou ‡ I. Mantellini § Abstract We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results even with respect to an axiomatic convergence, whose...

The evolution of an integrated mobile communication environment enables service deployment and content delivery offered by independent providers through heterogeneous network infrastructures. In a few months, a mobile user will be able to access value added services through several wireless public access networks (i.e., 3G cellular, Wireless LAN or WAN) belonging to the same or different operat...

When a simple real-valued estimation of distribution algorithm (EDA) with Gaussian model and maximum likelihood estimation of parameters is used, it converges prematurely even on the slope of the fitness function. The simplest way of preventing premature convergence by multiplying the variance estimate by a constant factor k each generation is studied. Recent works have shown that when increasi...

The search ability of an Evolutionary Algorithm (EA) depends on the variation among the individuals in the population [3, 4, 8]. Maintaining an optimal level of diversity in the EA population is imperative to ensure that progress of the EA search is unhindered by premature convergence to suboptimal solutions. Clearer understanding of the concept of population diversity, in the context of evolut...

Aktuğlu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and Gönül [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, x 1+x , y 1+y , ( x 1+x )2+( y 1+y )2....