Article
Mathematics, Applied
Jun Zhou, Pieter J. Barendrecht, Michael Barton, Jiri Kosinka
Summary: We investigate quadrature rules for quadrilateral Gregory patches, providing numerical and symbolic rules for the associated polynomial/rational functions as well as their derivatives and products. This allows for a wider use of Gregory patches in numerical simulations.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Statistics & Probability
Stephen G. Walker
Summary: We provide an explicit construction of variables from an infinitely divisible bivariate gamma distribution. This construction sheds further light on these distributions and their infinitely divisible property using independent gamma and Poisson random variables. The extension to multivariate gamma infinitely divisible variables and a negative binomial case are also provided.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Economics
Alexis Akira Toda
Summary: The paper introduces a simple nonparametric calibration method for discrete distributions, reducing the need for parametric assumptions. Results suggest that assuming normal instead of nonparametric shocks can lead to a reduction in equity premium and overweighting in stock portfolios.
COMPUTATIONAL ECONOMICS
(2021)
Article
Geochemistry & Geophysics
Xu Liu, Lan Du, Shuwen Xu
Summary: This letter introduces an adaptive detector specifically designed for sub-Gaussian symmetric alpha-stable sea clutter background using a GLRT-based approach. The detection method utilizes Fox's H-function to formulate the PDF of the SGS alpha S distribution and proposes a closed-form expression for test statistics based on the H-function. Experimental results demonstrate the effectiveness of the proposed detector in both simulated and measured data scenarios.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
(2022)
Article
Mathematics
Christian Berg, Stamatis Koumandos, Henrik L. Pedersen
Summary: The study shows that many special functions are 2nd-order generalized Stieltjes functions and therefore completely monotonic on a logarithmic scale. This includes the Laplace transform of various functions, ratios of Gamma functions, and the remainders in asymptotic expansions of the double Gamma function.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics, Applied
Jaehyuk Choi, Yeda Du, Qingshuo Song
Summary: A new numerical integration method is proposed in this study, which efficiently approximates the generalized hyperbolic distribution and accurately computes related expectations. It can also directly sample generalized hyperbolic random variables. The accuracy of the methods is demonstrated through numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yunfei Xia, Michael Grabchak
Summary: The methodology introduced in this study focuses on simulating and estimating parameters of multivariate tempered stable distributions, with a specific emphasis on the bivariate case. The approach involves an approximation through discretization of the spectral measure, which is demonstrated through analysis of two bivariate financial datasets related to exchange rates - standard currencies and cryptocurrencies. The results of this approximation are applicable to a wide range of multivariate infinitely divisible distributions.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2022)
Article
Mathematics, Applied
Luisa Fermo, Maria Grazia Russo, Giada Serafini
Summary: This paper considers the generalized Love integral equation and proposes a Nystrom method based on a mixed quadrature rule for its approximation. The stability and convergence of the numerical procedure are discussed in suitable weighted spaces, with the efficiency of the method shown through numerical tests.
NUMERICAL ALGORITHMS
(2021)
Article
Engineering, Mechanical
Felipe Igea, Alice Cicirello
Summary: Multi-modal distributions of physics-based model parameters are common in engineering, but traditional sampling techniques struggle to accurately capture them with limited simulations. This can lead to numerical errors in assessing structures under uncertainty. To overcome this, a cyclical annealing schedule is proposed for the Variational Bayes Monte Carlo (VBMC) method, improving exploration and finding high probability areas in multi-modal distributions. Comparisons with other algorithms show that the proposed cyclical VBMC outperforms in terms of accuracy and required model runs.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Statistics & Probability
Yasuyuki Hamura, Kaoru Irie, Shonosuke Sugasawa
Summary: In this paper, we propose a novel blocked Gibbs sampler for the matrix generalized inverse Gaussian (MGIG) distributions based on the Cholesky decomposition. We mathematically prove that the full conditionals of the diagonal and unit lower-triangular matrices are univariate generalized inverse Gaussian and multivariate normal distributions, respectively. The computational efficiency of the proposed Gibbs sampler is demonstrated through simulation studies and data analysis.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2023)
Article
Statistics & Probability
Ben Salah Nahla
Summary: This paper characterizes the real power of the convolution set of X+Y, where X and Y are two independent random variables with specific distributions. The obtained results generalize the case for Y being Gamma or Negative Binomial distributed.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Article
Mathematics
S. Bettin, S. Drappeau
Summary: The framework provides a simple way to prove two-term asymptotic expansions for Fourier integrals, applicable to many basic cases and particularly relevant to Levy's continuity theorem. It also has applications to limit laws related to rational continued fraction coefficients.
Article
Engineering, Multidisciplinary
Ning Zhang, Hong Zheng, Liang Yang, Wenan Wu, Chi Yuan
Summary: This paper presents a numerically stable one-point quadrature rule for the stiffness matrix and mass matrix of the three-dimensional numerical manifold method (3D NMM). The rule simplifies the integration over irregularly shaped manifold elements, overcomes locking issues, and does not cause spurious modes in modal analysis. The proposed method is suitable for 3D NMM meshes generated from a regular grid and has been numerically tested to validate its accuracy improvements and stability.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Noureddin Sakhavi, Nowrouz Mohammad Nouri
Summary: The study demonstrates that the generalized velocity model can reduce the sensitivity of multipath phased array flowmeters to flow field, enhancing measurement accuracy. The average relative errors are within 1.64% under symmetric and asymmetric flow fields.
Article
Statistics & Probability
Witold Bednorz, Rafal Martynek
Summary: This paper provides a full characterization of the expected suprema of infinitely divisible processes and positively settles the conjecture posed by M. Talagrand.
ANNALS OF PROBABILITY
(2022)
Article
Computer Science, Artificial Intelligence
Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W. Hogg, Michael O'Neil
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2016)
Article
Computer Science, Interdisciplinary Applications
Jun Lai, Leslie Greengard, Michael O'Neil
JOURNAL OF COMPUTATIONAL PHYSICS
(2017)
Article
Computer Science, Interdisciplinary Applications
Manas Rachh, Andreas Klockner, Michael O'Neil
JOURNAL OF COMPUTATIONAL PHYSICS
(2017)
Article
Mathematics, Applied
Michael O'Neil
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2018)
Article
Mathematics, Applied
Jun Lai, Leslie Greengard, Michael O'Neil
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2018)
Article
Computer Science, Interdisciplinary Applications
Michael O'Neil, Antoine J. Cerfon
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Engineering, Electrical & Electronic
Charles L. Epstein, Zydrunas Gimbutas, Leslie Greengard, Andreas Kloeckner, Michael O'Neil
IEEE TRANSACTIONS ON MAGNETICS
(2013)
Article
Computer Science, Interdisciplinary Applications
Charles L. Epstein, Leslie Greengard, Michael O'Neil
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Computer Science, Interdisciplinary Applications
Dhairya Malhotra, Antoine Cerfon, Lise-Marie Imbert-Gerard, Michael O'Neil
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Computer Science, Interdisciplinary Applications
Jun Lai, Michael O'Neil
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Mathematics, Applied
Felipe Vico, Leslie Greengard, Michael O'Neil, Manas Rachh
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)