Related papers: New Checkable Conditions for Moment Determinacy of…
We consider univariate distributions with finite moments of all positive orders. The moment problem is to determine whether or not a given distribution is uniquely determined by the sequence of its moments. There is a huge literature on…
One of the ways to characterize a probability distribution is to show that it is moment-determinate, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends entirely on the behaviour of the…
We show first that there are intrinsic relationships among different conditions, old and recent, which lead to some general statements in both the Stieltjes and the Hamburger moment problems. Then we describe checkable conditions and prove…
The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be…
Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of…
We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent easily checkable condition on the rate of growth of the moments. We use…
This paper aims at finding conditions on a Hamburger or Stieltjes moment sequence, under which the change of at most a finite number of its entries produces another sequence of the same type. It turns out that a moment sequence allows all…
The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly an infinite family of probability densities with the same sequence of moments. In this paper, the notion of $q$-moment…
Lin's condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin's condition for functions of random variables have emerged. In this…
The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the…
This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On…
We consider a normalized indeterminate Hamburger moment sequence s which is supposed to be Stieltjes. We revisit old results about determinacy/indeterminacy in the sense of Stieltjes for s and we prove some new results about the concepts…
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
We exploit results on the classical Stieltjes moment problem to obtain completely explicit necessary and sufficient conditions for the photon number distribution p(n) of a radiation field mode to be classical. These conditions are given in…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence…
Conditional specification of distributions is a developing area with many applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…
Probability densities that are not uniquely determined by their moments are said to be "moment-indeterminate", or "M-indeterminate". Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is…