scholarly journals Moment-sequence transforms

2021 ◽  
Author(s):  
Alexander Belton ◽  
Dominique Guillot ◽  
Apoorva Khare ◽  
Mihai Putinar
Keyword(s):  
Moment Sequence

On weak convergence within the hnbue family of life distributions

1984 ◽  
Vol 21 (03) ◽  
pp. 654-660 ◽  
Author(s):  
Sujit K. Basu ◽  
Manish C. Bhattacharjee
Keyword(s):  
Weak Convergence ◽  
Exponential Distribution ◽  
Limiting Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moment Sequence ◽  
Positive Order ◽  
Life Distributions ◽  
Necessary And Sufficient

We show that the HNBUE family of life distributions is closed under weak convergence and that weak convergence within this family is equivalent to convergence of each moment sequence of positive order to the corresponding moment of the limiting distribution. A necessary and sufficient condition for weak convergence to the exponential distribution is given, based on a new characterization of exponentials within the HNBUE family of life distributions.

scholarly journals Operators that admit a moment sequence, II

2006 ◽  
Vol 135 (6) ◽  
pp. 1763-1767 ◽  
Author(s):  
B. Chevreau ◽  
I. B. Jung ◽  
E. Ko ◽  
C. Pearcy
Keyword(s):  
Moment Sequence

scholarly journals The Logarithmic Skew-Normal Distributions are Moment-Indeterminate

2009 ◽  
Vol 46 (3) ◽  
pp. 909-916 ◽  
Author(s):  
Gwo Dong Lin ◽  
Jordan Stoyanov
Keyword(s):  
Positive Integer ◽  
Heavy Tails ◽  
Moment Sequence ◽  
Normal Distributions ◽  
Problem Of Moments ◽  
Skew Normal Distributions ◽  
Skew Normal

We study the class of logarithmic skew-normal (LSN) distributions. They have heavy tails; however, all their moments of positive integer orders are finite. We are interested in the problem of moments for such distributions. We show that the LSN distributions are all nonunique (moment-indeterminate). Moreover, we explicitly describe Stieltjes classes for some LSN distributions; they are families of infinitely many distributions, which are different but have the same moment sequence as a fixed LSN distribution.

scholarly journals Hamburger and Stieltjes Moment Problems for Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
L. Lemnete-Ninulescu
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Moment Problems ◽  
Moment Sequence ◽  
Bounded Operators ◽  
Necessary And Sufficient ◽  
Stieltjes Moment Sequence

Solutions to some operator-valued, unidimensional, Hamburger and Stieltjes moment problems in this paper are given. Necessary and sufficient conditions on some sequences of bounded operators being Hamburger, respectively, Stieltjes operator-valued moment sequences are obtained. The determinateness of the operator-valued Hamburger and Stieltjes moment sequence is studied.

scholarly journals The Logarithmic Skew-Normal Distributions are Moment-Indeterminate

2009 ◽  
Vol 46 (03) ◽  
pp. 909-916 ◽  
Author(s):  
Gwo Dong Lin ◽  
Jordan Stoyanov
Keyword(s):  
Positive Integer ◽  
Heavy Tails ◽  
Moment Sequence ◽  
Normal Distributions ◽  
Problem Of Moments ◽  
Skew Normal Distributions ◽  
Skew Normal

We study the class of logarithmic skew-normal (LSN) distributions. They have heavy tails; however, all their moments of positive integer orders are finite. We are interested in the problem of moments for such distributions. We show that the LSN distributions are all nonunique (moment-indeterminate). Moreover, we explicitly describe Stieltjes classes for some LSN distributions; they are families of infinitely many distributions, which are different but have the same moment sequence as a fixed LSN distribution.

scholarly journals The complex moment problem: determinacy and extendibility

2019 ◽  
Vol 124 (2) ◽  
pp. 263-288 ◽  
Author(s):  
Dariusz Cichoń ◽  
Jan Stochel ◽  
Franciszek Hugon Szafraniec
Keyword(s):  
Partial Solution ◽  
Positive Definite ◽  
Lattice Points ◽  
Moment Sequence ◽  
Representing Measure ◽  
Straight Line Passing ◽  
Straight Line ◽  
Plane Algebraic Curve ◽  
Line Passing ◽  
Point Set

Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is determinate and its only representing measure has no atom at $0$. The question of converting the relation is posed as an open problem. A partial solution to this problem is established when at least one of representing measures is supported in a plane algebraic curve whose intersection with every straight line passing through $0$ is at most one point set. Further study concerns representing measures whose supports are Zariski dense in $\mathbb{C} $ as well as complex moment sequences which are constant on a family of parallel “Diophantine lines”. All this is supported by a bunch of illustrative examples.

scholarly journals Limiting Distributions for a Class Of Diminishing Urn Models

2012 ◽  
Vol 44 (1) ◽  
pp. 87-116 ◽  
Author(s):  
Markus Kuba ◽  
Alois Panholzer
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Urn Models ◽  
Moment Sequence ◽  
Limiting Distributions ◽  
Sampling Without Replacement ◽  
The Moment

In this work we analyze a class of 2 × 2 Pólya-Eggenberger urn models with ball replacement matrix and c = pa with . We determine limiting distributions by obtaining a precise recursive description of the moments of the considered random variables, which allows us to deduce asymptotic expansions of the moments. In particular, we obtain limiting distributions for the pills problem a = c = d = 1, originally proposed by Knuth and McCarthy. Furthermore, we also obtain limiting distributions for the well-known sampling without replacement urn, a = d = 1 and c = 0, and generalizations of it to arbitrary and c = 0. Moreover, we obtain a recursive description of the moment sequence for a generalized problem.

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