Abstract The prediction and correction of systematic errors in direct spectral estimation from irregularly sampled data taken a stochastic process is investigated. Different sampling schemes are investigated, which lead to such an irregular the observed process. Both kinds considered, with non-equidistant intervals continuous distribution and, on other hand, nominally equidistant missing indivi...

Tolerance intervals are widely used in industrial applications. So far attention has been mainly focused on the construction of tolerance intervals for continuous distributions. In this paper we introduce a unified analytical approach to the construction of tolerance intervals for discrete distributions in exponential families with quadratic variance functions. These tolerance intervals are sho...

Numerous bamboo species collectively flower and seed at dramatically extended, regular intervals - some as long as 120 years. These collective seed releases, termed 'masts', are thought to be a strategy to overwhelm seed predators or to maximise pollination rates. But why are the intervals so long, and how did they evolve? We propose a simple mathematical model that supports their evolution as ...

If two solutions Y ≤ Z of the DARE are given then the set of solutions X with Y ≤ X ≤ Z can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y . The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.

One-sided con&dence intervals in the binomial, negative binomial, and Poisson distributions are considered. It is shown that the standard Wald interval su4ers from a serious systematic bias in the coverage and so does the one-sided score interval. Alternative con&dence intervals with better performance are considered. The coverage and length properties of the con&dence intervals are compared th...

The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate...

The solution of linear discrete ill-posed problems is very sensitive to perturbations in the data. Confidence intervals for solution coordinates provide insight into the sensitivity. This paper presents an efficient method for computing confidence intervals for large-scale linear discrete ill-posed problems. The method is based on approximating the matrix in these problems by a partial singular...

We use discrete quadratic Lyapunov functions to design controllers for a class of systems where time intervals between state measurements are longer than time intervals between control actions and different components of the state vector are not measured at the same time. The discrete Lyapunov function is a discretization of a continuous Lyapunov function assumed to be known for the idealized s...

Let T be any time scale such that 0, 1 be subset of T. The concept of dynamic equations on time scales can build bridges between differential and difference equations. This concept not only gives us unified approach to study the boundary value problems on discrete intervals with uniform step size and real intervals but also gives an extended approach to study on discrete case with non uniform s...