The truncated Hausdorff moment problem solved by using kernel density functions

Athanassoulis, G. A.; Gavriliadis, P. N.

doi:10.1016/s0266-8920(02)00012-7

Cited by 49 publications

(63 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, an excessive value of the number N of kernel pdfs increases the computational complexity of the procedure, so as to be excessive if compared with the obtained improvement. Also note that Equation (16) in full rigor is valid only whenf X (x) = f X (x), and this relationship is verified for not too small values N of kernel pdfs. Extensive numerical experimentation has shown that generally a good choice is represented by N = 20-100.…”

Section: Discretization Of the Mpmentioning

confidence: 73%

“…In the proposed approach, following Athanassoulis and Gavriliadis [16,17], the kernel density function f K X (x; x i , h i ) has been chosen as a basis pdf, and then Equation (8) becomeŝ…”

Section: The Kdrmentioning

confidence: 99%

“…In the analysis of system (16), first insight has to be focused about the parameters of the KDR. A first step is related to the choice of the 'window of analysis'ˆ ⊆ , that is, the range of the pdf under examination where we choose the 'centers' x i of the kernel pdfs and therefore such that x i ∈ˆ .…”

Section: Discretization Of the Mpmentioning

confidence: 99%

“…. , N −1, while a good choice of the bandwidth is represented from h = q x, with q = In system (16), the number of moments M gives the data information, whereas the number N of kernel density functions gives the resolution used for the recovery of the target pdf f X (x). Obviously, if the number of moment M increases, we have more information, and then the approximation should be better; unfortunately the MP is strongly ill-conditioned, and therefore it is not an easy task to determine good approximations of the target pdf when the higher moments are also known.…”

Section: Discretization Of the Mpmentioning

confidence: 99%

See 3 more Smart Citations

Efficient evaluation of the pdf of a random variable through the kernel density maximum entropy approach

Alibrandi

Ricciardi

2008

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIn this paper, a new approach for the evaluation of the probability density function (pdf) of a random variable from the knowledge of its lower moments is presented. At first the classical moment problem (MP) is revisited, which gives the conditions such that the assigned sequence of sample moments represent really a sequence of moments of any distribution. Then an alternative approach is presented, termed as the kernel density maximum entropy (MaxEnt) method by the authors, which approximates the target pdf as a convex linear combination of kernel densities, transforming the original MP into a discrete MP, which is solved through a MaxEnt approach. In this way, simply solving a discrete MaxEnt problem, not requiring the evaluation of numerical integrals, an approximating pdf converging toward the MaxEnt pdf is obtained. The method is first demonstrated by approximating some known analytical pdfs (the chi-square and the Gumbel pdfs) and then it is applied to some experimental engineering problems, namely for modelling the pdf of concrete strength, the circular frequency and the damping ratio of strong ground motions, the extreme wind speed in Messina's Strait region. All the developed numerical applications show the goodness and efficacy of the proposed procedure.

show abstract

Section: Discretization Of the Mpmentioning

confidence: 73%

“…In the proposed approach, following Athanassoulis and Gavriliadis [16,17], the kernel density function f K X (x; x i , h i ) has been chosen as a basis pdf, and then Equation (8) becomeŝ…”

Section: The Kdrmentioning

confidence: 99%

Section: Discretization Of the Mpmentioning

confidence: 99%

Section: Discretization Of the Mpmentioning

confidence: 99%

See 2 more Smart Citations

Efficient evaluation of the pdf of a random variable through the kernel density maximum entropy approach

Alibrandi

Ricciardi

2008

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Without loss of generality we may and will suppose that [−a, a] = [−1, 1]. In practise, observations of moments appear especially in quantum physics (see for instance Ash and Mc Donald (2003) and Mead and Papanicolaou (1983)), image analysis (see Teague (1980)), engineering mechanics (see Athanassoulis and Gavriliadis (2002)) and all the references therein). We shall give now some concrete examples of the application of the problem of moments, in which either one can have access directly to moments to reconstruct the unknown function at stake or the moment problem appears in the line of reasoning.…”

Section: Introductionmentioning

confidence: 99%

A statistical minimax approach to the Hausdorff moment problem

Ngoc

2008

Inverse Problems

View full text Add to dashboard Cite

The purpose of this paper is to study the problem of estimating a compactly supported function from noisy observations of its moments in an ill-posed inverse problem framework. We provide a statistical approach to the famous Hausdorff classical moment problem. We prove a lower bound on the rate of convergence of the mean integrated squared error and provide an estimator which attains minimax rate over the corresponding smoothness classes.

show abstract

Droplet breakage and coalescence in liquid–liquid dispersions: Comparison of different kernels with EQMOM and QMOM

Gao

Buffo

et al. 2016

AIChE Journal

View full text Add to dashboard Cite

Droplet coalescence and breakage in turbulent liquid–liquid dispersions is simulated by using computational fluid dynamics (CFD) and population balance modeling. The multifractal (MF) formalism that takes into account internal intermittency was here used for the first time to describe breakage and coalescence in a surfactant‐free dispersion. The log‐normal Extended Quadrature Method of Moments (EQMOM) was for the first time coupled with a CFD multiphase solver. To assess the accuracy of the model, predictions are compared with experiments and other models (i.e., Coulalogou and Tavlarides kernels and Quadrature Method of Moments [QMOM]). EQMOM and QMOM resulted in similar predictions, but EQMOM provides a continuous reconstruction of the droplet‐size distribution. Transient predictions obtained with the MF kernels result in a better agreement with the experiments. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2293–2311, 2017

show abstract

The truncated Hausdorff moment problem solved by using kernel density functions

Cited by 49 publications

References 14 publications

Efficient evaluation of the pdf of a random variable through the kernel density maximum entropy approach

Efficient evaluation of the pdf of a random variable through the kernel density maximum entropy approach

A statistical minimax approach to the Hausdorff moment problem

Droplet breakage and coalescence in liquid–liquid dispersions: Comparison of different kernels with EQMOM and QMOM

Contact Info

Product

Resources

About