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## Statistics of random processes I: General theory

### Metrika (1983-12-01) 30: 100 , December 01, 1983

## Eight-run two-level factorial designs under dependence

### Metrika (1998-12-01) 48: 127-139 , December 01, 1998

### Abstract.

Dependent observations commonly arise in factorial experiments. Apart from main-effects two-level designs formed by the Cheng & Steinberg reverse foldover algorithm, which are known to be very efficient designs under dependence using the *D*-criterion, little is known about other designs, models and criteria, and the range of possible behaviour. In this paper, we investigate in detail 8-run two-level designs.

## Bounds for the mean residual life function of a k-out-of-n system

### Metrika (2011-11-01) 74: 361-380 , November 01, 2011

In the reliability studies, *k*-out-of-*n* systems play an important role. In this paper, we consider sharp bounds for the mean residual life function of a *k*-out-of-*n* system consisting of *n* identical components with independent lifetimes having a common distribution function *F*, measured in location and scale units of the residual life random variable *X*_{t} = (*X*−*t*|*X* > *t*). We characterize the probability distributions for which the bounds are attained. We also evaluate the so obtained bounds numerically for various choices of *k* and *n*.

## On axiomatic characterization of some non-additive measures of information

### Metrika (1977-12-01) 24: 23-34 , December 01, 1977

An axiomatic characterization of non-additive measures of information associated with a pair of probability distributions having the same number of elements has been given. This quantity under additional suitable postulates leads to the non-additive Entropy, Directed-Divergence and Inaccuracy of one or more parameters.

## The lattice structure of nonlinear congruential pseudorandom numbers

### Metrika (1993-12-01) 40: 115-120 , December 01, 1993

Several known deficiencies of the classical linear congruential method for generating uniform pseudorandom numbers led to the development of nonlinear congruential pseudorandom number generators. In the present paper a general class of nonlinear congruential methods with prime power modulus is considered. It is proved that these generators show certain undesirable linear structures, too, which stem from the composite nature of the modulus.

## Sequential estimation of normal mean under asymmetric loss function with a shrinkage stopping rule

### Metrika (1998-09-01) 48: 53-59 , September 01, 1998

### Abstract.

The problem of estimating a normal mean with unknown variance is considered under an asymmetric loss function such that the associated risk is bounded from above by a known quantity. In the absence of a fixed sample size rule, a sequential stopping rule and two sequential estimators of the mean are proposed and second-order asymptotic expansions of their risk functions are derived. It is demonstrated that the sample mean becomes asymptotically inadmissible, being dominated by a shrinkage-type estimator. Also a shrinkage factor is incorporated in the stopping rule and similar inadmissibility results are established.

## The multiresolution histogram

### Metrika (1997-01-01) 46: 41-57 , January 01, 1997

We introduce a new method for locally adaptive histogram construction that doesn’t resort to a standard distribution and is easy to implement: the multiresolution histogram. It is based on a*L*_{2} analysis of the mean integrated squared error with Haar wavelets and hence can be associated with a multiresolution analysis of the sample space.

## Dreistufige klienste Quadrate —einige numerische Ergebnisse

### Metrika (1973-12-01) 20: 193-195 , December 01, 1973

## A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings

### Metrika (2011-07-01) 74: 33-54 , July 01, 2011

Let *U*_{1}, *U*_{2}, . . . , *U*_{n–1} be an ordered sample from a Uniform [0,1] distribution. The non-overlapping uniform spacings of order *s* are defined as
$${G_{i}^{(s)} =U_{is} -U_{(i-1)s}, i=1,2,\ldots,N^\prime, G_{N^\prime+1}^{(s)} =1-U_{N^\prime s}}$$
with notation *U*_{0} = 0, *U*_{n} = 1, where
$${N^\prime=\left\lfloor n/s\right\rfloor}$$
is the integer part of *n*/*s*. Let
$${ N=\left\lceil n/s\right\rceil}$$
be the smallest integer greater than or equal to *n*/*s*, *f*_{m} (*u*), *m* = 1, 2, . . . , *N*, be a sequence of real-valued Borel-measurable functions. In this article a Cramér type large deviation theorem for the statistic
$${f_{1,n} (nG_{1}^{(s)})+\cdots+f_{N,n} (nG_{N}^{(s)} )}$$
is proved.