On certain random polygons of large areas.
Displaying 121 – 140 of 235
On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane
Tomáš Mrkvička, Jan Rataj (2009)
Kybernetika
A method of estimation of intrinsic volume densities for stationary random closed sets in based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the...
On geometric-optical projection of spatial particle size distribution
Vratislav Horálek (1985)
Kybernetika
On invariants of random planar endomorphisms
Teimuraz Aliashvili (2003)
Banach Center Publications
We estimate the expected value of the gradient degree of certain Gaussian random polynomials in two variables and discuss its relations with some other numerical invariants of random polynomials
On mean value theorems for small geodesic spheres in Riemannian manifolds
Masanori Kôzaki (1992)
Czechoslovak Mathematical Journal
On random convex hulls
Jan Mycielski (1987)
Colloquium Mathematicae
On random fractals with infinite branching: definition, measurability, dimensions
Artemi Berlinkov (2013)
Annales de l'I.H.P. Probabilités et statistiques
We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
On random subsets of projective spaces
Wojciech Kordecki, Tomasz Łuczak (1991)
Colloquium Mathematicae
On set covariance and three-point test sets
Jan Rataj (2004)
Czechoslovak Mathematical Journal
The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic...
On some estimation variances in spatial statistics
Joël Chadeuf, Viktor Beneš (1994)
Kybernetika
On some random convex sets
R. Jajte (1971)
Colloquium Mathematicae
On testing of general random closed set model hypothesis
Tomáš Mrkvička (2009)
Kybernetika
A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the -parallel sets to . The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation...
On the Convex Hull of Uniform Random Points in a Simple d-Polytope.
J.A. Wieacker, F. Affentranger (1991)
Discrete & computational geometry
On the covering by small random intervals
Ai-Hua Fan, Jun Wu (2004)
Annales de l'I.H.P. Probabilités et statistiques
On the decomposition of particle size distribution in the extraction replica method
Vratislav Horálek (1981)
Aplikace matematiky
This paper deals with the method for evaluating exposures of nickel alloy structures containing both extracted and sectioned particles. The presented stereological model makes it possible to estimate two unknown spatial parameters, the mean value of the particle size distribution and the depth of etching with the use of the information obtained from the combined structure of the exposures.
On the distance random variable
G. Trybuś (1974)
Applicationes Mathematicae
On the Distribution of a Distance Function on the Sphere.
M. Yaqub, A.M. Khan (1980)
Metrika
On the Expected Number of k-Sets.
I. Bárány, W. Steiger (1994)
Discrete & computational geometry
On the isotropic constant of marginals
Grigoris Paouris (2012)
Studia Mathematica
We show that if μ₁, ..., μₘ are log-concave subgaussian or supergaussian probability measures in , i ≤ m, then for every F in the Grassmannian , where N = n₁ + ⋯ + nₘ and n< N, the isotropic constant of the marginal of the product of these measures, , is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.
On the Modality of Convex Polygons.
K. Abrahamson (1990)
Discrete & computational geometry