Operations research, ISSN 1526-5463, 2019, Volume 67, Issue 5, pp. 1321 - 1327

In many operations management problems, the decisions are truncated by random variables...

two-part fee structure | risk aversion | dependent supply capacity uncertainty | inventory management | stochastic optimization | DEMAND | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | INVENTORY | DYNAMIC CAPACITY MANAGEMENT | Inventory control | Costs (Law) | Analysis

two-part fee structure | risk aversion | dependent supply capacity uncertainty | inventory management | stochastic optimization | DEMAND | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | INVENTORY | DYNAMIC CAPACITY MANAGEMENT | Inventory control | Costs (Law) | Analysis

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2019, Volume 351, pp. 643 - 666

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables...

Quadrature | Uncertainty quantification | Leja sequence | Interpolation | Polynomial chaos expansion | Nataf transformation | TRANSFORMATION | APPROXIMATION | QUANTIFICATION | NUMERICAL APPROACH | DIMENSIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | STOCHASTIC COLLOCATION METHOD | ENGINEERING, MULTIDISCIPLINARY | PARTIAL-DIFFERENTIAL-EQUATIONS | CONSTRUCTION | CONVERGENCE | Analysis | Algorithms | Differential equations | Construction | Approximation | Independent variables | Ill-conditioning (mathematics) | Mapping | Transformations (mathematics) | Dependent variables | Collocation methods | Measurement methods | Polynomials | Galerkin method | Random variables | Performance degradation | Methods

Quadrature | Uncertainty quantification | Leja sequence | Interpolation | Polynomial chaos expansion | Nataf transformation | TRANSFORMATION | APPROXIMATION | QUANTIFICATION | NUMERICAL APPROACH | DIMENSIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | STOCHASTIC COLLOCATION METHOD | ENGINEERING, MULTIDISCIPLINARY | PARTIAL-DIFFERENTIAL-EQUATIONS | CONSTRUCTION | CONVERGENCE | Analysis | Algorithms | Differential equations | Construction | Approximation | Independent variables | Ill-conditioning (mathematics) | Mapping | Transformations (mathematics) | Dependent variables | Collocation methods | Measurement methods | Polynomials | Galerkin method | Random variables | Performance degradation | Methods

Journal Article

Annals of Physics, ISSN 0003-4916, 01/2018, Volume 388, pp. 350 - 381

.... Most previous work studied systems of independent random variables, and relied on the independence in their analyses...

Fourier transform | Benford’s law | Dependent random variables | Mellin transform | Fragmentation | Benford's law | DISTRIBUTIONS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | CONVERGENCE | UNIFORM-DISTRIBUTION | Mathematics - Probability

Fourier transform | Benford’s law | Dependent random variables | Mellin transform | Fragmentation | Benford's law | DISTRIBUTIONS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | CONVERGENCE | UNIFORM-DISTRIBUTION | Mathematics - Probability

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 18

Acceptable random variables introduced by Giuliano Antonini et al. (J. Math. Anal. Appl. 338:1188-1203, 2008) form a class of dependent random variables that contains negatively dependent random variables as a particular case...

Analysis | F $\mathcal{F}$ -acceptable random variables | conditional complete convergence | Mathematics, general | 62G20 | Mathematics | Applications of Mathematics | exponential inequalities | 60F15 | F-acceptable random variables | DEPENDENT RANDOM-VARIABLES | COMPLETE CONVERGENCE | MATHEMATICS | MATHEMATICS, APPLIED | PROBABILITY-INEQUALITIES | SUMS | Conditioning | Random variables | Asymptotic properties | Acceptability | Inequalities

Analysis | F $\mathcal{F}$ -acceptable random variables | conditional complete convergence | Mathematics, general | 62G20 | Mathematics | Applications of Mathematics | exponential inequalities | 60F15 | F-acceptable random variables | DEPENDENT RANDOM-VARIABLES | COMPLETE CONVERGENCE | MATHEMATICS | MATHEMATICS, APPLIED | PROBABILITY-INEQUALITIES | SUMS | Conditioning | Random variables | Asymptotic properties | Acceptability | Inequalities

Journal Article

Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 6/2019, Volume 43, Issue 3, pp. 1161 - 1165

In this paper, we present some general results concerning complete convergence for arrays of dependent random variables, dominated in a sense by independent random variables...

Engineering | Life Sciences, general | Complete convergence | Chemistry/Food Science, general | Materials Science, general | Earth Sciences, general | Dependent random variables | Engineering, general | Physics, general | 60F15 | MULTIDISCIPLINARY SCIENCES

Engineering | Life Sciences, general | Complete convergence | Chemistry/Food Science, general | Materials Science, general | Earth Sciences, general | Dependent random variables | Engineering, general | Physics, general | 60F15 | MULTIDISCIPLINARY SCIENCES

Journal Article

Computational Statistics, ISSN 0943-4062, 06/2017, Volume 32, Issue 2, pp. 559 - 583

This paper proposes a new methodology to model uncertainties associated with functional random variables...

DENSITY | STATISTICS & PROBABILITY | MODEL | Analysis | Algorithms | Parameter estimation | Uncertainty | Methodology | Computer simulation | Dependent variables | Decomposition | Mathematical models | Random variables | Probability density functions | Statistics | Statistics Theory | Mathematics

DENSITY | STATISTICS & PROBABILITY | MODEL | Analysis | Algorithms | Parameter estimation | Uncertainty | Methodology | Computer simulation | Dependent variables | Decomposition | Mathematical models | Random variables | Probability density functions | Statistics | Statistics Theory | Mathematics

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 02/2019, Volume 344, pp. 910 - 937

This paper is concerned with uncertainty quantification analysis of complex systems subject to dependent input random variables...

Multivariate orthogonal polynomials | ANOVA | Non-product-type probability measures | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTEGRATION | Boundary value problems | Error analysis | Statistical analysis | Independent variables | Decomposition | Complex systems | Variance | Thermal expansion | Dependent variables | Dependence | Eigenvalues | Polynomials | Random variables | Linear equations | Formulas (mathematics) | Uncertainty analysis

Multivariate orthogonal polynomials | ANOVA | Non-product-type probability measures | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTEGRATION | Boundary value problems | Error analysis | Statistical analysis | Independent variables | Decomposition | Complex systems | Variance | Thermal expansion | Dependent variables | Dependence | Eigenvalues | Polynomials | Random variables | Linear equations | Formulas (mathematics) | Uncertainty analysis

Journal Article

Test (Madrid, Spain), ISSN 1863-8260, 2014, Volume 23, Issue 3, pp. 607 - 629

...) random variables are presented, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality...

62G05 | Marcinkiewicz–Zygmund type inequality | Statistical Theory and Methods | Statistics, general | Statistics | Nonparametric regression model | Complete consistency | Rosenthal type inequality | Complete convergence | Statistics for Business/Economics/Mathematical Finance/Insurance | Widely orthant-dependent random variables | 60F15 | 60E05 | INEQUALITIES | FIXED-DESIGN REGRESSION | Marcinkiewicz-Zygmund type inequality | NOD SEQUENCE | STATISTICS & PROBABILITY | ESTIMATOR | ARRAYS | WEIGHTED SUMS | CONSISTENCY | PRECISE LARGE DEVIATIONS | UNIFORM ASYMPTOTICS | STRONG LAW | Studies | Regression analysis | Weight function | Inequalities | Consistency | Regression | Random variables | Arrays | Estimators | Convergence

62G05 | Marcinkiewicz–Zygmund type inequality | Statistical Theory and Methods | Statistics, general | Statistics | Nonparametric regression model | Complete consistency | Rosenthal type inequality | Complete convergence | Statistics for Business/Economics/Mathematical Finance/Insurance | Widely orthant-dependent random variables | 60F15 | 60E05 | INEQUALITIES | FIXED-DESIGN REGRESSION | Marcinkiewicz-Zygmund type inequality | NOD SEQUENCE | STATISTICS & PROBABILITY | ESTIMATOR | ARRAYS | WEIGHTED SUMS | CONSISTENCY | PRECISE LARGE DEVIATIONS | UNIFORM ASYMPTOTICS | STRONG LAW | Studies | Regression analysis | Weight function | Inequalities | Consistency | Regression | Random variables | Arrays | Estimators | Convergence

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2020, Volume 371, p. 112703

In this paper, we present methods of obtaining single moments of order statistics arising from possibly dependent and non-identically distributed discrete random variables...

Discrete distributions | Dependent non-identically distributed random variables | Moments | Coherent systems | Reliability | Order statistics | LIFETIMES | MATHEMATICS, APPLIED | SIGNATURES | BOUNDS | EXPECTATION | COMPONENTS

Discrete distributions | Dependent non-identically distributed random variables | Moments | Coherent systems | Reliability | Order statistics | LIFETIMES | MATHEMATICS, APPLIED | SIGNATURES | BOUNDS | EXPECTATION | COMPONENTS

Journal Article

Metrika, ISSN 0026-1335, 2015, Volume 78, Issue 3, pp. 295 - 311

...) random variables, which includes sequences of negatively associated random variables as a special case...

Weak law of large numbers | Negatively superadditive dependent random variables | Complete consistency | WEIGHTED SUMS | CONVERGENCE THEOREM | NONPARAMETRIC MULTIPLE-REGRESSION | SEQUENCES | FIXED-DESIGN REGRESSION | LINEAR-TIME SERIES | STATISTICS & PROBABILITY | QUADRATIC-FORMS | ASSOCIATION | Equality

Weak law of large numbers | Negatively superadditive dependent random variables | Complete consistency | WEIGHTED SUMS | CONVERGENCE THEOREM | NONPARAMETRIC MULTIPLE-REGRESSION | SEQUENCES | FIXED-DESIGN REGRESSION | LINEAR-TIME SERIES | STATISTICS & PROBABILITY | QUADRATIC-FORMS | ASSOCIATION | Equality

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2018, Volume 31, Issue 4, pp. 2432 - 2445

Assuming conditions on factorial cumulants, we estimate the closeness of distribution of a sum of nonnegative integer-valued m-dependent random variables to the class of all infinitely divisible laws...

Uniform Kolmogorov theorem | Total variation norm | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Compound Poisson distribution | m -dependent variables | Local norm | 60F05 | m-dependent variables | STATISTICS & PROBABILITY

Uniform Kolmogorov theorem | Total variation norm | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Compound Poisson distribution | m -dependent variables | Local norm | 60F05 | m-dependent variables | STATISTICS & PROBABILITY

Journal Article

Stochastics, ISSN 1744-2508, 05/2016, Volume 88, Issue 4, pp. 606 - 621

...) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented...

Negatively superadditive dependent random variables | complete moment convergence | complete convergence | DEPENDENT RANDOM-VARIABLES | MATHEMATICS, APPLIED | INEQUALITIES | STATISTICS & PROBABILITY | SUMS | Randomness | Paper | Random variables | Arrays | Probability theory | Convergence

Negatively superadditive dependent random variables | complete moment convergence | complete convergence | DEPENDENT RANDOM-VARIABLES | MATHEMATICS, APPLIED | INEQUALITIES | STATISTICS & PROBABILITY | SUMS | Randomness | Paper | Random variables | Arrays | Probability theory | Convergence

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 3/2016, Volume 110, Issue 1, pp. 251 - 268

Some exponential probability inequalities for widely negative orthant dependent (WNOD, in short) random variables are established, which can be treated as very...

Complete moment convergence | Complete convergence | Theoretical, Mathematical and Computational Physics | Widely negative orthant dependent random variables | Mathematics, general | Mathematics | Applications of Mathematics | Marcinkiewicz–Zygmund type strong law of large numbers | 60F15 | 60E05 | NOD SEQUENCE | Marcinkiewicz-Zygmund type strong law of large numbers | BAHADUR REPRESENTATION | ARRAYS | DEPENDENT RANDOM-VARIABLES | WEIGHTED SUMS | MATHEMATICS | PRECISE LARGE DEVIATIONS | MODELS | THEOREMS | UNIFORM ASYMPTOTICS | Mathematical analysis | Probability theory | Inequalities | Random variables | Arrays | Statistics | Convergence

Complete moment convergence | Complete convergence | Theoretical, Mathematical and Computational Physics | Widely negative orthant dependent random variables | Mathematics, general | Mathematics | Applications of Mathematics | Marcinkiewicz–Zygmund type strong law of large numbers | 60F15 | 60E05 | NOD SEQUENCE | Marcinkiewicz-Zygmund type strong law of large numbers | BAHADUR REPRESENTATION | ARRAYS | DEPENDENT RANDOM-VARIABLES | WEIGHTED SUMS | MATHEMATICS | PRECISE LARGE DEVIATIONS | MODELS | THEOREMS | UNIFORM ASYMPTOTICS | Mathematical analysis | Probability theory | Inequalities | Random variables | Arrays | Statistics | Convergence

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 12/2019, Volume 48, Issue 23, pp. 5673 - 5681

Generalizations of the Central Limit Theorem to N dependent random variables often assume that the dependence falls off...

Central limit theorem | Vasicek | dependent random variables | credit portfolio | 91G10 | 60F05 | 60E05 | Economic models | Economic analysis | Loans | Statistical analysis | Dependent variables | Normal distribution | Dependence | Random variables | Risk analysis | Convergence

Central limit theorem | Vasicek | dependent random variables | credit portfolio | 91G10 | 60F05 | 60E05 | Economic models | Economic analysis | Loans | Statistical analysis | Dependent variables | Normal distribution | Dependence | Random variables | Risk analysis | Convergence

Journal Article

Communications in Mathematics and Statistics, ISSN 2194-6701, 3/2019, Volume 7, Issue 1, pp. 1 - 23

We consider the tail behavior of the product of two dependent random variables X and $$\Theta $$ Θ...

Copula | Dependent product | Ruin probabilities | 62E20 | Mathematics, general | 60G70 | Mathematics | Statistics, general | Regular variation | RISKS | BEHAVIOR | MODEL | WEIGHTED SUMS | MATHEMATICS | PROBABILITY | SUBEXPONENTIALITY | HEAVY-TAILED INSURANCE | ASYMPTOTICS | FINITE-TIME

Copula | Dependent product | Ruin probabilities | 62E20 | Mathematics, general | 60G70 | Mathematics | Statistics, general | Regular variation | RISKS | BEHAVIOR | MODEL | WEIGHTED SUMS | MATHEMATICS | PROBABILITY | SUBEXPONENTIALITY | HEAVY-TAILED INSURANCE | ASYMPTOTICS | FINITE-TIME

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 12

...(i) of random variables satisfying the Rosenthal type inequality are established under some mild conditions...

weighted sums | complete convergence | Rosenthal type inequality | DEPENDENT RANDOM-VARIABLES | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | LIMIT-THEOREMS | SURE CONVERGENCE | ARRAYS | Theorems | Inequalities | Texts | Random variables | Formulas (mathematics) | Convergence | Sums

weighted sums | complete convergence | Rosenthal type inequality | DEPENDENT RANDOM-VARIABLES | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | LIMIT-THEOREMS | SURE CONVERGENCE | ARRAYS | Theorems | Inequalities | Texts | Random variables | Formulas (mathematics) | Convergence | Sums

Journal Article

PloS one, ISSN 1932-6203, 2015, Volume 10, Issue 9, p. e0137278

The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be...

ORGANIZATION | DISTANCE | INTEGRATION | MATRICES | MULTIDISCIPLINARY SCIENCES | BRAIN | Models, Theoretical | Magnetic Resonance Imaging | Female | Male | Humans | Bayes Theorem | Cluster analysis | Neuroimaging | Brain | Data analysis | Neurosciences | Nuclear magnetic resonance--NMR | Balances (scales) | Computer simulation | Similarity measures | Time series | Brain mapping | Data processing | Covariance matrix | Clustering | Gene expression | Datasets | Magnetic resonance imaging | Covariance | Dependent variables | Functional magnetic resonance imaging | Mathematical models | Random variables | Bioinformatics | Bayesian analysis | Life Sciences | Bioengineering | Computer Science | Nuclear magnetic resonance | NMR

ORGANIZATION | DISTANCE | INTEGRATION | MATRICES | MULTIDISCIPLINARY SCIENCES | BRAIN | Models, Theoretical | Magnetic Resonance Imaging | Female | Male | Humans | Bayes Theorem | Cluster analysis | Neuroimaging | Brain | Data analysis | Neurosciences | Nuclear magnetic resonance--NMR | Balances (scales) | Computer simulation | Similarity measures | Time series | Brain mapping | Data processing | Covariance matrix | Clustering | Gene expression | Datasets | Magnetic resonance imaging | Covariance | Dependent variables | Functional magnetic resonance imaging | Mathematical models | Random variables | Bioinformatics | Bayesian analysis | Life Sciences | Bioengineering | Computer Science | Nuclear magnetic resonance | NMR

Journal Article

JOURNAL OF INEQUALITIES AND APPLICATIONS, ISSN 1029-242X, 04/2019, Volume 2019, Issue 1, pp. 1 - 17

The goal of this paper is to build complete convergence and complete integral convergence for END sequences of random variables under sub-linear expectation space...

Sub-linear expectation | DEPENDENT RANDOM-VARIABLES | MATHEMATICS | MATHEMATICS, APPLIED | LARGE NUMBERS | INEQUALITIES | Complete convergence | Complete integral convergence | STRONG LAW | END random variables | Markov processes | Theorems | Random variables | Integrals | Convergence

Sub-linear expectation | DEPENDENT RANDOM-VARIABLES | MATHEMATICS | MATHEMATICS, APPLIED | LARGE NUMBERS | INEQUALITIES | Complete convergence | Complete integral convergence | STRONG LAW | END random variables | Markov processes | Theorems | Random variables | Integrals | Convergence

Journal Article