On equivalence of weak convergence and moment convergence of life distributions

We investigate the equivalence of weak convergence and moment convergence of life distributions in a family which is larger than the HNBUE family. Also, we point out that within the HNBUE family the exponential distribution can be characterized by one value of its Laplace-Stieltjes transform.     

On distributions of functionals of the brownian motion stopped at the moment inverse to local time

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 30–47, 1992     

Structural decompositions of multivariate distributions with applications in moment and cumulant

We provide lattice decompositions for multivariate distributions. The lattice decompositions reveal the structural relationship between the Lancaster/Bahadur model and the model of Streitberg (Ann. Statist. 18 (1990) 1878). For multivariate categorical data, the decompositions allows modeling strategy for marginal inference. The theory discussed in this paper illustrates the concept of reproducibility, which was discussed in Liang et al. (J. Roy. Statist. Soc. Ser. B 54 (1992) 3). For the purpose of delineating the relationship between the various types of decompositions of distributions, we develop a theory of polytypefication, the generality of which is exploited to prove results beyond interaction.     

On the inversion of certain moment matrices

An explicit representation of the elements of the inverses of certain patterned matrices involving the moments of nonnegative weight functions is derived in this paper. It is shown that a sequence of monic orthogonal polynomials can be generated from a given weight function in terms of Hankel-type determinants and that the corresponding matrix inverse can be expressed in terms of their associated coefficients and orthogonality factors. This result enables one to obtain an explicit representation of a certain type of approximants which apply to a wide class of positive continuous functions. Convenient expressions for the coefficients of standard classical orthogonal polynomials such as Legendre, Jacobi, Laguerre and Hermite polynomials are also provided. Several examples illustrate the results.     

On the solution of the finite moment problem

In this work we propose a method to obtain the normal solution of the finite moment problem both in the absence and in the presence of linear boundary constraints. The method gives the normal solution as a linear combination of Jacobi polynomials and furnishes its coefficients in terms of the moments. A number of examples are given to illustrate the strength of the method.     

On the Stieltjes moment problem on semigroups

We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).     

On the second moment in Blachke's problem

Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 2, pp. 149–154, April–June, 1994.     

On the optimal mapping of distributions

We consider the problem of mappingXY, whereX andY have given distributions, so as to minimize the expected value of X–Y². This is equivalent to finding the joint distribution of the random variable (X, Y), with specified marginal distributions forX andY, such that the expected value of X–Y² is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases.     

On the support of tempered distributions

We show that, given a tempered distribution S whose Fourier transform is a function of polynomial growth, a point x in is outside the support of S if and only if the Fourier integral of S is summable in Bochner-Riesz means to zero uniformly on a neighbourhood of x. Received: 29 December 2005     

On the strong matrix Hamburger moment problem

We obtain necessary and sufficient conditions for the solvability of the strong matrix Hamburger moment problem. We describe all solutions of the moment problem by using the fundamental results of A. V. Shtraus on generalized resolvents of symmetric operators.     

On the stereological estimation of reduced moment measures

Recently, a new set of fundamental stereological formulae based on isotropically oriented probes through fixed points have been derived, the so-called nucleator estimation principle (cf. Jensen and Gundersen (1989, J. Microsc., 153, 249–267)). In the present paper, it is shown how a model-based version of these formulae leads to stereological estimators of reduced moment measures of stationary and isotropic random sets in ⁿ .