In this paper we consider the regression problem for random sets of the Boolean-model type. Regression modeling of the Boolean random sets using some explanatory variables are classified according to the type of these variables as propagation, growth or propagation-growth models. The maximum...

A coherent set of explicit approximations is presented for the variance of planar area and volume estimators obtained under systematic geometric sampling. For planar objects (e.g. a land plot, or a tissue section), sampling is considered with test systems of points, lines, segments, stripes, or...

In this paper we derive a lower bound on the average complexity of the Simplex-Method as a solution-process for linear programs (LP) of the type:<Equation ID="Equ1"> <EquationSource Format="TEX"/> </Equation> We assume these problems to be randomly generated according to the Rotation-Symmetry-Model: *Let a <Subscript>1</Subscript>,…,a <Subscript>m</Subscript>, v be distributed independently,...</subscript></subscript></equation>

Distributional properties are considered of the typical cell of stationary iterated tessellations (SIT), which are generated by stationary Poisson-Voronoi tessellations (SPVT) and stationary Poisson line tessellations (SPLT), respectively. Using Neveu’s exchange formula, the typical cell of...