Article
Mathematics, Interdisciplinary Applications
Oscar Lorenzo Olvera Astivia, Kroc Edward
Summary: This paper explores some theoretical aspects of the g-and-h family of distributions, which are widely used for modeling non-normal data. The study shows that a popular multivariate generalization of the g-and-h distribution may result in marginal distributions that do not follow the g-and-h distribution. It also reveals that multiple sets of (g,h) parameters can correspond to the same population skewness and excess kurtosis. Additionally, the multivariate generalizations of g-and-h distributions found in literature are special cases of Gaussian copula distributions.
BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY
(2022)
Article
Mathematics, Applied
Aisha Fayomi, Ehab M. Almetwally, Maha E. Qura
Summary: This paper presents a new family of bivariate continuous Lomax generators, called the BFGMLG family, constructed using univariate Lomax generator families and the FGM copula. The paper derives several statistical properties of the proposed bivariate family, such as marginals, conditional distribution, moments, correlation, and reliability function. The study also introduces special submodels based on different baseline distributions and suggests a multivariate version of the continuous FGMLG family. Bayesian and maximum likelihood methods are employed to estimate model parameters, and a Monte Carlo simulation evaluates the performance. The practical application of the proposed bivariate family is demonstrated through the analysis of four data sets.
Article
Mathematics, Applied
Baishuai Zuo, Chuancun Yin, Narayanaswamy Balakrishnan
Summary: Inspired by Stein's lemma, this paper derives two expressions for the joint moments of elliptical distributions, and presents new formulae for calculating expectations of product of normally distributed random variables. It also provides simplified expressions of E[X(1)(2)f (X)] for multivariate Student-t, logistic and Laplace distributions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Multidisciplinary Sciences
Sreenivasa Rao Jammalamadaka, Emanuele Taufer, Gyorgy H. Terdik
Summary: This paper provides a systematic and comprehensive treatment for deriving general expressions of moments and cumulants for spherically and elliptically symmetric multivariate distributions, with detailed discussions on the multivariate t-distribution and related skew-t distribution.
Article
Mathematics, Applied
Nenad Antonic, Marko Erceg, Marin Misur
Summary: The text introduces the definition of anisotropic order distributions on manifolds and their immediate properties. It also discusses the Schwartz kernel theorem for such distributions and their applications, particularly focusing on H-distributions and their potential in further applications to partial differential equations.
ANALYSIS AND APPLICATIONS
(2021)
Article
Engineering, Civil
Guoqing Huang, Ruili Liu, Min Liu, Haitao Zheng
Summary: A method based on the multivariate AR-GARCH model is proposed to model and simulate the multivariate nonstationary wind speed process. The BEKK model is adopted to maintain the positive definiteness of the conditional covariance matrix, and numerical simulations as well as measured data are used to validate the accuracy of the proposed method.
JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS
(2021)
Article
Mathematics, Applied
N. Antonic, M. Erceg
Summary: H-measures and semiclassical (Wigner) measures have been widely used in problems involving L-2 weakly converging sequences since their introduction in the early 1990s. While they are similar, they are not generalizations of each other, with the main difference being the presence of a characteristic length in semiclassical measures and the absence of one in H-measures. The recent introduction of one-scale H-measures encapsulates properties of both measures. This paper aims to develop this theory in the L-p setting (p epsilon (1, infinity)) by constructing one-scale H-distributions and extending semiclassical measures using the Wigner transform.
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Bo Zhu, Shumin Zhang, Huifen Ge, Chengfu Ye
Summary: This paper investigates the reliability of interconnection networks in multiprocessing systems and proposes two new connectivity parameters to accurately measure the network's reliability. Experimental results on hypercube networks are provided.
Article
Multidisciplinary Sciences
Luciano Souza, Wilson Rosa de Oliveira, Cicero Carlos Ramos de Brito, Christophe Chesneau, Renan Fernandes, Tiago A. E. Ferreira
Summary: This paper introduces a new class of trigonometric distributions based on the secant function, which modifies the tails and overall skewness features of well-known distributions. The unique four-parameter continuous distribution of this class, defined with the Kumaraswamy-Weibull distribution as the baseline, is emphasized. The model parameters are estimated using the maximum likelihood method. A numerical simulation study shows that the proposed secant Kumaraswamy-Weibull model outperforms important competitors.
Article
Computer Science, Interdisciplinary Applications
Matieyendou Lamboni
Summary: This paper derives practical dependency functions for classical multivariate distributions, which are useful for uncertainty quantification, sensitivity analysis, and simulation of random variables. A method for selecting efficient sampling functions using multivariate sensitivity analysis is provided, and the approach is illustrated through numerical simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Guangshuai Zhou, Chuancun Yin
Summary: In this study, a new class of skewed distributions called extended mean mixtures of multivariate normal (EMMN) distributions is constructed. The basic properties, parameter estimation method, and application to special cases of this distribution family are derived. Simulation experiments and real data fitting illustrate the performance and flexibility of this distribution family.
Article
Automation & Control Systems
Richard G. Brereton
Summary: The traditional use of p values is described for univariate distributions and Design of Experiments, with additional applications in chemometrics. The difficulties of interpreting non-orthogonal variables are discussed, along with simulations showing how p values decrease as correlation decreases. High correlation between variables can lead to incorrect conclusions about individual variable significance.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2021)
Article
Engineering, Chemical
Johan Nordstrand
Summary: Capacitive deionization (CDI) has been widely adopted as a desalination method in recent years. This work presents a new theory and software for CDI simulations that consider individual ionic species and material effects. The results demonstrate the effectiveness of this approach and provide insights into the limitations of traditional methods. The comprehensive software and video tutorial provided in this work facilitate future research in CDI processes.
Article
Mathematics, Interdisciplinary Applications
Jin Zhao, Zubair Ahmad, Eisa Mahmoudi, E. H. Hafez, Marwa M. Mohie El-Din
Summary: Statistical distributions, especially heavy-tailed distributions, are crucial for modeling actuarial and financial data. A new power transformation method is introduced to model heavy-tailed financial data, demonstrating its effectiveness through a submodel.
Article
Mathematics
Raul Alejandro Moran-Vasquez, Silvia L. P. Ferrari
Summary: Truncated elliptical distributions are important in statistics, playing a crucial role in the study of multivariate distributions, particularly the multivariate truncated normal and truncated t distributions. Deriving statistical properties of these distributions can help establish new properties in related distributions such as the multivariate truncated slash and truncated power exponential distributions.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2021)
