The paper is motivated by the stochastic comparison of the reliability of non-repairable $k$-out-of-$n$ systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let $U_i,i=1,...,n,$ be positive independent random variables with common distribution $F$. For ${\lambda }_i\>0$ and $\mu \>0$, let consider $X_i=U_i/{\lambda }_i$ and $Y_i=U_i/\mu ,i=1,...,n$. Remark that this is no more than a change of scale for each term. For $k\in \{1,2,...,n\},$ let us define $X_{k:n}$ to be the $k$th order statistics...

The paper is motivated by the stochastic comparison of the reliability of non-repairable k-out-of-n systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let Ui,i = 1,...,n, be positive independent random variables with common distribution F. For λi > 0 and µ > 0, let consider Xi = Ui/λi and Yi = Ui/µ, i = 1,...,n. Remark that this is no more than a change of scale for each...

Let $P$ be a discrete multidimensional probability distribution over a finite set of variables $N$ which is only partially specified by the requirement that it has prescribed given marginals $\{P_A;A\in 𝒮\}$, where $𝒮$ is a class of subsets of $N$ with $\bigcup 𝒮=N$. The paper deals with the problem of approximating $P$ on the basis of those given marginals. The divergence of an approximation $\widehat{P}$ from $P$ is measured by the relative entropy $H\left(P\right|\widehat{P})$. Two methods for approximating $P$ are compared. One of them uses formerly introduced concept of...

Let $\{X_{n,j},1\le j\le m\left(n\right),n\ge 1\}$ be an array of rowwise pairwise negative quadrant dependent mean 0 random variables and let $0<b_n\to \infty$. Conditions are given for ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}/b_n\to 0$ completely and for ${max}_{1\le k\le m\left(n\right)}\left|{\sum }_{j=1}^k{X}_{n,j}\right|/b_n\to 0$ completely. As an application of these results, we obtain a complete convergence theorem for the row sums ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}^{*}$ of the dependent bootstrap samples $\{\{X_{n,j}^{*},1\le j\le m\left(n\right)\},n\ge 1\}$ arising from a sequence of i.i.d. random variables $\{X_n,n\ge 1\}$.

Complete $f$-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric...

To obtain a robust version of exponential and Holt-Winters smoothing the idea of $M$-estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. 11 (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller forecast...

One of the main goals in times series analysis is to forecast future values. Many forecasting methods have been developed and the most successful are based on the concept of exponential smoothing, based on the principle of obtaining forecasts as weighted combinations of past observations. Classical procedures to obtain forecast intervals assume a known distribution for the error process, what is not true in many situations. A bootstrap methodology can be used to compute distribution free forecast...

The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.

The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.

Data depth is an important concept of nonparametric approach to multivariate data analysis. The main aim of the paper is to review possible applications of the data depth, including outlier detection, robust and affine-equivariant estimates of location, rank tests for multivariate scale difference, control charts for multivariate processes, and depth-based classifiers solving discrimination problem.

We consider here a multivariate sample Xj = (X1.j &gt; ... &gt; Xi.j), 1 ≤ j ≤ n, where the Xj, 1 ≤ j ≤ n, are independent i-dimensional extremal vectors with suitable unknown location and scale parameters λ and δ respectively. Being interested in linear estimation of these parameters, we consider the multivariate sample Zj, 1 ≤ j ≤ n, of the order statistic of largest values and their concomitants, and the best linear unbiased estimators of λ and δ based on such multivariate sample. Computational...

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

Se define un estimador no paramétrico, recursivo, de la función de regresión r(x) = E(Y/X = x), que se calcula a partir de un conjunto de n observaciones {(X1,Yi): i = 1, ..., n} del vector aleatorio (X,Y). Bajo la hipótesis de que los datos son idénticamente distribuidos pero no necesariamente independientes, lo que permite utilizar el estimador definido para estimar la función de autorregresión de una serie de tiempo, se obtienen resultados sobre la consistencia puntual débil (en probabilidad)...