Search results for "Transform"
showing 10 items of 3975 documents
Phase transformation kinetics in d-dimensional grains-containing systems: diffusion-type model
1998
Abstract An analytical approach to the phase transformation in d-dimensional grains-containing complex systems is offered. It is based on considering the mechanism of surface material exchange among neighbouring grains as the so-called state-dependent diffusion process, where the diffusion function is related to the magnitude of the grain boundary. The approach proposed deals with the kinetics of that ensemble under circumstances of a volume increase of the new phase or microstructure. Probabilistic characteristics of the process are derived and analyzed. A comparison with 2D modelling of similar kind is presented for the 3D case, and some possible practical realizations of the situation un…
Posterior moments and quantiles for the normal location model with Laplace prior
2021
We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter η in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of η.
Hitting straight lines by compound Poisson process paths
1990
In a recent article Mallows and Nair (1989,Ann. Inst. Statist. Math.,41, 1–8) determined the probability of intersectionP{X(t)=αt for somet≥0} between a compound Poisson process {X(t), t≥0} and a straight line through the origin. Using four different approaches (direct probabilistic, via differential equations and via Laplace transforms) we extend their results to obtain the probability of intersection between {X(t), t≥0} and arbitrary lines. Also, we display a relationship with the theory of Galton-Watson processes. Additional results concern the intersections with two (or more) parallel lines.
Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range
2014
A Bayesian solution is suggested for the modelling of spatial point patterns with inhomogeneous hard-core radius using Gaussian processes in the regularization. The key observation is that a straightforward use of the finite Gibbs hard-core process likelihood together with a log-Gaussian random field prior does not work without penalisation towards high local packing density. Instead, a nearest neighbour Gibbs process likelihood is used. This approach to hard-core inhomogeneity is an alternative to the transformation inhomogeneous hard-core modelling. The computations are based on recent Markovian approximation results for Gaussian fields. As an application, data on the nest locations of Sa…
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
2011
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set of invariant measures in the small-noise limit. The aim of this study is essentially to point out that this statement leads to the existence, as the noise intensity is small, of one unique…
Fractional calculus approach to the statistical characterization of random variables and vectors
2009
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…
Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review
1999
The paper reviews recent contributions to the statistical inference methods, tests and estimates, based on the generalized median of Oja. Multivariate analogues of sign and rank concepts, affine invariant one-sample and two-sample sign tests and rank tests, affine equivariant median and Hodges–Lehmann-type estimates are reviewed and discussed. Some comparisons are made to other generalizations. The theory is illustrated by two examples.
Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
2006
In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estima…
Lattices and dual lattices in optimal experimental design for Fourier models
1998
Number-theoretic lattices, used in integration theory, are studied from the viewpoint of the design and analysis of experiments. For certain Fourier regression models lattices are optimal as experimental designs because they produce orthogonal information matrices. When the Fourier model is restricted, that is a special subset of the full factorial (cross-spectral) model is used, there is a difficult inversion problem to find generators for an optimal design for the given model. Asymptotic results are derived for certain models as the dimension of the space goes to infinity. These can be thought of as a complexity theory connecting designs and models or as special type of Nyquist sampling t…
Block–Savits Characterization and Star Ordering of Exponential Mixtures
2008
Block and Savits (1980) established a characterization of life distributions using the Laplace transform. In this article, we remark that one of the necessary conditions to be IFRA distribution is equivalent to the star ordering of exponential mixtures. It leads to the definition of two new classes of life distributions, called LIFR and LIFRA, and their dual classes: LDFR and LDFRA. It occurs that these classes have many useful aging properties and preserve known reliability operations. Properties of the classes are studied and relations with known classes are established.