Article
Computer Science, Interdisciplinary Applications
Liang Han, Haijun Liu, Wengang Zhang, Lin Wang
Summary: This study evaluates the performance of different models in geo-material parametric data and finds that copula models generally have lower model uncertainty compared to the conventional multivariate normal distribution model, with the elliptical copula model ranking first. For a balanced evaluation of performance and complexity, the conventional multivariate normal distribution model is favored.
COMPUTERS AND GEOTECHNICS
(2023)
Article
Statistics & Probability
Wenli Deng, Jinglong Wang, Riquan Zhang
Summary: This paper proposes a measure of concordance that considers all random variables simultaneously and deduces its distribution and other relevant properties. It also introduces a nonparametric test method for the independence of multivariate random variables.
JOURNAL OF MULTIVARIATE ANALYSIS
(2022)
Article
Mathematics
Xi Liu, Yiqiao Jin, Yifan Yang, Xiaoqing Pan
Summary: This paper investigates the marginal and conditional distributions of a multivariate folded normal distribution and proves the equivalence of independence and non-correlation for it. A numerical approach using the R language is also presented to fit the distribution, with an examination of the accuracy of the estimated mean and variance parameters. Lastly, a real data application on body mass index is provided.
Article
Multidisciplinary Sciences
Raul Alejandro Moran-Vasquez, Alejandro Roldan-Correa, Daya K. Nagar
Summary: We propose a new multivariate skewed distribution with positive support, called the quantile-based multivariate log-normal distribution, which has interpretable parameters in terms of marginal quantiles and associations between variables. We derive various statistical properties of this distribution, such as transformations, mixed moments, expected value, covariance matrix, mode, Shannon entropy, and Kullback-Leibler divergence. We also discuss parameter estimation and evaluate the model fitting using Mahalanobis-type distances, with an application to children data.
Article
Automation & Control Systems
Gholamreza Hesamian, Mohamad Ghasem Akbari
Summary: This study proposed a fuzzy statistical test for the mean and variance-covariance matrix of a multivariate normal distribution with fuzzy random variables. Concepts such as fuzzy type-I error, fuzzy type-II error, fuzzy power, non-fuzzy significance level, and fuzzy p-value were extended, and a degree-based criterion was suggested for comparing fuzzy p-values and making decisions on accepting or rejecting hypotheses. The effectiveness of the proposed fuzzy hypothesis test was examined through numerical examples.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2022)
Article
Engineering, Multidisciplinary
Roberto Candela, Antonio Gattuso, Massimo Mitolo, Eleonora Riva Sanseverino, Gaetano Zizzo
Summary: This article reviews the special bonding techniques for medium voltage and high-voltage cables, aiming to reduce sheath currents, limit copper losses, and decrease cable ampacity. The evolution and application of these techniques are analyzed through literature review and MATLAB/Simulink simulations.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS
(2021)
Article
Multidisciplinary Sciences
Raul Alejandro Moran-Vasquez, Duvan Humberto Catano Salazar, Daya K. Nagar
Summary: This article studies several properties of the truncated multivariate skew-normal distribution, obtaining distributional results through affine transformations, marginalization, and conditioning, and establishing the log-concavity of the joint probability density function.
Article
Mathematics
Thomas L. Toulias, Christos P. Kitsos
Summary: This paper investigates and discusses the behavior of KL divergence under the gamma-GND distribution, including its symmetry and differences between various distributions. Additionally, it explores three symmetrized forms of KL divergence and their corresponding differences in the gamma-GND family.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2021)
Article
Mathematics
Guillermo Martinez-Florez, Artur J. Lemonte, German Moreno-Arenas, Roger Tovar-Falon
Summary: A new bivariate absolutely continuous probability distribution, BVUSHN distribution, is introduced in this paper. The main properties of the new distribution are studied and the BVUSHN regression model is also presented. Parameter estimation is performed using the maximum likelihood method and the two-step estimation method. A small Monte Carlo simulation study is conducted to evaluate the behavior of the estimation method and the properties of the estimators. Two applications with real data are provided to demonstrate the usefulness of the proposals.
Article
Engineering, Civil
Yelu Zhou, Dongming Zhang, Hongwei Huang, Yadong Xue
Summary: This paper investigates the application of normal transformation methods related to marginal probability density functions (PDFs) in constructing multivariate normal distributions. By comparing three different types of normal transformation methods, it is found that all three methods are applicable within the framework of multivariate normal distribution. Based on the consistency between the normality of the transformed variables and the performance of the constructed multivariate normal distribution, the Johnson transformation method is recommended.
ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING
(2022)
Article
Mathematics, Applied
Aurora Monter-Pozos, Elizabeth Gonzalez-Estrada
Summary: The skew normal distribution is a flexible and applicable distribution for modeling symmetric and skew data sets. This paper proposes a method based on data transformation to test the hypothesis that a sample follows a skew normal distribution, and provides formulas for calculating critical values. The analysis of real data sets demonstrates the plausibility of the skew normal distribution in modeling the behavior of real data.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics
Alexey Kudryavtsev, Oleg Shestakov
Summary: The study focuses on the generalizations of known mathematical objects for adequate models, with emphasis on the gamma class of distributions. The gamma class is a useful tool for modeling real processes, with properties like infinite divisibility and stability. The study introduces estimators for parameters of the gamma-exponential distribution, utilizing a modified method of moments based on logarithmic moments calculated from the Mellin transform. Confidence intervals for estimated parameters are constructed, with potential applications in probabilistic models based on continuous distributions with unbounded non-negative support.
Article
Computer Science, Interdisciplinary Applications
Erik Hintz, Marius Hofert, Christiane Lemieux
Summary: Efficient algorithms for computing distribution function, (log-)density function, and estimating parameters of multivariate normal variance mixtures are introduced. Numerical examples demonstrate the suggested algorithms are quite fast, even for high dimensions around 1000, accurately estimating distribution function and log-densities.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2021)
Article
Mathematics
Leonardo Barrios, Yolanda M. Gomez, Osvaldo Venegas, Inmaculada Barranco-Chamorro, Hector W. Gomez
Summary: In this paper, an extension of the power half-normal distribution is proposed, which is built on the application of slash methodology for positive random variables. The new model exhibits greater kurtosis and a heavier right tail compared to the conventional power half-normal distribution. The probability density, survival and hazard rate functions are studied, and its moments, skewness, kurtosis coefficients, and properties related to reliability are obtained. It is proven that the new model can be expressed as a scale mixture of a power half-normal distribution and a uniform distribution. The new model also holds the power half-normal distribution as a limit case when its parameter tends to infinity. The parameters in the model are estimated using the method of moments and maximum likelihood. A simulation study is conducted to demonstrate the good performance of maximum likelihood estimators. Additionally, two real applications to survival and fatigue fracture data are presented, where the proposed model outperforms other models.
Article
Mathematics, Applied
Cedric Heuchenne, Gilles Mordant
Summary: This paper proposes new tests for comparing multivariate probability distributions by transforming the problem into one-dimensional classical tests using measure transportation theory. The distribution-free tests developed in this study are computationally efficient and outperform existing techniques in terms of power functions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics
Neslihan Kilar, Yilmaz Simsek, H. M. Srivastava
Summary: The paper utilizes the Laplace transform and generating functions to obtain interesting infinite series representations for the Apostol-type parametrically generalized polynomials. In addition to recurrence relations, the method of generating functions also provides various formulas, identities, relations, and combinatorial sums for these polynomials and other special numbers and polynomials. These findings have connections to higher order Apostol-Bernoulli polynomials, Apostol-Euler polynomials, Apostol-Genocchi polynomials, cosine and sine-Bernoulli polynomials, cosine and sine-Euler polynomials, lambda-array-type polynomials, lambda-Stirling numbers, polynomials C-n(x,y)Cn(x,y), and polynomials S-n(x,y)Sn(x,y). Furthermore, the paper presents new recurrence relations for these special polynomials and numbers.
Article
Mathematics
H. M. Srivastava, Sarem. H. H. Hadi, Maslina Darus
Summary: In this article, a generalized q-Bernardi integral operator (or (p, q)-Bernardi integral operator) is introduced and investigated for analytic and p-valent (or multivalent) functions. Subclasses of gamma-uniformly q starlike and q-convex p-valent functions of order n are defined using this q-integral operator. Various properties and characteristics, such as coefficient estimates, convex linear combination, growth and distortion theorems, and the radii of gamma-uniformly starlikeness, convexity and close-to-convexity, are then investigated for functions belonging to these subclasses.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Multidisciplinary Sciences
Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Juan Luis G. Guirao, Dumitru Baleanu, Eman Al-Sarairah, Rashid Jan
Summary: The class of symmetric function interacts extensively with other types of functions, particularly with the class of positivity of functions. In this study, we propose a positive analysis technique to analyze a specific class of Liouville-Caputo difference equations of fractional-order with extremal conditions. By utilizing difference conditions, we derive relative minimum and maximum through monotonicity results. The obtained monotonicity results are verified by solving two numerical examples.
Article
Mathematics
Ana Maria Acu, Ioan Rasa, Hari M. Srivastava
Summary: The paper discusses a specific discrete probability distribution and its properties and applications. It then extends this distribution to a family of discrete distributions with two parameters and examines the properties of the new distributions.
Article
Mathematics, Applied
Hari Mohan Srivastava, Timilehin Gideon Shaba, Gangadharan Murugusundaramoorthy, Abbas Kareem Wanas, Georgia Irina Oros
Summary: In this paper, a new subclass of normalized functions that are analytic and univalent in the open unit disk is introduced and studied. The functions in this class satisfy a geometric criterion and are associated with the Hohlov operator. The coefficient bounds, as well as upper estimates for the Fekete-Szego functional and the Hankel determinant, are investigated.
Article
Mathematics, Applied
Pshtiwan Othman Mohammed, Christopher S. S. Goodrich, Hari Mohan Srivastava, Eman Al-Sarairah, Y. S. Hamed
Summary: In this article, we investigate the relationship between the sign of a Liouville-Caputo-type difference operator and the monotone behavior of the function it acts on. Additionally, we provide an example to demonstrate the application and validation of the results presented in this study.
Article
Mathematics, Applied
Isra Al-Shbeil, Adriana Catas, Hari Mohan Srivastava, Najla Aloraini
Summary: In this paper, two new subclasses of bi-univalent functions are introduced using the q-Hermite polynomials. The bounds of the initial coefficients of the Taylor-Maclaurin series and the Fekete-Szego functional associated with the new classes are established, and the implications of the findings are discussed.
Editorial Material
Multidisciplinary Sciences
Hari Mohan Srivastava
Summary: This article provides an introductory overview of Bessel polynomials and generalized Bessel polynomials, their applications in the classical wave equation, recent developments in quantum extensions, and investigations of hypergeometric polynomials.
Article
Mathematics, Applied
Zahra Eidinejad, Reza Saadati, Hari M. Srivastava
Summary: In this article, a new class of fuzzy control functions is applied to approximate a Cauchy additive mapping in fuzzy Banach space. Furthermore, the isomorphisms defined in the unital FBS are investigated. By introducing specific functions and selecting the optimal control function, the Cauchy-Optimal stability (C-O-stability) for all defined mappings is evaluated.
Article
Mathematics, Applied
Hari Mohan Srivastava, Isra Al-Shbeil, Qin Xin, Fairouz Tchier, Shahid Khan, Sarfraz Nawaz Malik
Summary: By utilizing q-fractional derivative operator and bi-close-to-convex functions, a new subclass of A is defined, where A is a class that contains normalized analytic functions in the open unit disk E and is rotationally invariant or symmetric. Using the Faber polynomial expansion technique, the lth coefficient bound is determined for the functions in this subclass. The article provides further explanation for the first few coefficients of bi-close-to-convex functions defined by q-fractional derivative, and emphasizes on some well-known outcomes of the major findings.
Article
Mathematics, Applied
Hari M. M. Srivastava, Firdous A. A. Shah, Huzaifa L. L. Qadri, Waseem Z. Z. Lone, Musadiq S. S. Gojree
Summary: The Hilbert transform, a widely used linear operator in filter design, signal processing, and communication theory, has limitations in representing signals in generalized domains. To overcome this, we propose a novel integral transform called the quadratic-phase Hilbert transform and study its fundamental properties, relationship with the quadratic-phase Fourier transform, convolution theorem, and the Bedrosian theorem. Simulation results confirm the validity and accuracy of our proposed transform.
Article
Multidisciplinary Sciences
Hari Mohan Srivastava, Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Artion Kashuri, Nejmeddine Chorfi
Summary: This article discusses a general family of weighted fractional integral operators and establishes numerous reverse Minkowski inequalities using this operator. Symmetry is crucial in understanding and investigating convexity and inequality, as it provides insightful explanations, clearer explanations, and useful methods for learning key mathematical ideas. The kernel of the general family of weighted fractional integral operators is related to various extensions and generalizations of the Mittag-Leffler function and the Hurwitz-Lerch zeta function. The article delves into the applications of fractional-order integral and derivative operators in mathematical and engineering sciences and introduces novel applications involving the Digamma function.
Article
Multidisciplinary Sciences
Muhammad Zain Yousaf, Hari Mohan Srivastava, Muhammad Abbas, Tahir Nazir, Pshtiwan Othman Mohammed, Miguel Vivas-Cortez, Nejmeddine Chorfi
Summary: This paper presents a numerical solution for fourth-order singular singularly-perturbed boundary and initial value problems using a novel quintic B-spline approximation approach. By applying a quasi-linearization method, the non-linear problems are transformed into linear problems, resulting in more accurate results. The proposed method is demonstrated to converge uniformly over the whole domain and performs better compared to existing approaches.
Article
Mathematics, Interdisciplinary Applications
Khaled Mohammed Saad, Hari Mohan Srivastava
Summary: In this article, the authors investigate the numerical solutions of several fractional-order models of the multi-space coupled Korteweg-De Vries equation involving different kernels. They transform these models into a set of differential equations and use spectral collocation approach to solve them. The precision of the numerical solution is verified by calculating the error involved. The use of spectral methods is shown to be beneficial in providing accurate solutions with exponential convergence.
FRACTAL AND FRACTIONAL
(2023)
Article
Multidisciplinary Sciences
Ayesha Mahmood, Hari Mohan Srivastava, Muhammad Abbas, Farah Aini Abdullah, Pshtiwan Othman Mohammed, Dumitru Baleanu, Nejmeddine Chorfi
Summary: The study uses the extended direct algebraic technique to generate various forms of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, providing visual representations through 2D, 3D, and density plots. This research expands our understanding of optical solitons in birefringent fibres and offers potential new approaches for studying other nonlinear systems.
Article
Statistics & Probability
Tsung- Lin, Wan-Lun Wang
Summary: This paper derives explicit expressions for the moments of truncated multivariate normal/independent distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is conducted to validate the proposed formulae for five selected members of the distributions.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Tao Qiu, Qintong Zhang, Yuanyuan Fang, Wangli Xu
Summary: This article introduces a method for testing the homogeneity of two random vectors. The method involves selecting two subspaces and projecting them onto one-dimensional spaces, using the Cramer-von Mises distance to construct the test statistic. The performance is enhanced by repeating this procedure and the effectiveness is demonstrated through numerical simulations.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Alfredo Alegria, Xavier Emery
Summary: This study contributes to covariance modeling by proposing new parametric families of isotropic matrix-valued functions that exhibit non-monotonic behaviors, such as hole effects and cross-dimples. The benefit of these models is demonstrated on a bivariate dataset of airborne particulate matter concentrations.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Kento Egashira, Kazuyoshi Yata, Makoto Aoshima
Summary: This study investigates the asymptotic properties of hierarchical clustering in different settings, including high-dimensional, low-sample-size scenarios. The results show that hierarchical clustering exhibits good asymptotic properties under practical settings for high-dimensional data. The study also extends the analysis to consider scenarios where both the dimension and sample size approach infinity, and generalizes the concept of populations in multiclass HDLSS settings.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Marlene Baumeister, Marc Ditzhaus, Markus Pauly
Summary: This paper introduces a more robust multivariate analysis method by using general quantiles, particularly the median, instead of the traditional mean, and applies and validates this method on various factorial designs. The effectiveness of this method is demonstrated through theoretical and simulation studies on small and moderate sample sizes.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Chuancun Yin, Narayanaswamy Balakrishnan
Summary: The family of multivariate skew-normal distributions has interesting properties, which also hold for a general class of skew-elliptical distributions.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Gaspard Bernard, Thomas Verdebout
Summary: In this paper, we address the problem of testing the relationship between the eigenvalues of a scatter matrix in an elliptical distribution. Using the Le Cam asymptotic theory, we show that the non-specification of nuisance parameters has an asymptotic cost for testing the relationship. We also propose a distribution-free signed-rank test for this problem.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
