Applied Mathematics and Computation, ISSN 0096-3003, 09/2013, Volume 220, pp. 482 - 486

In this study, Fibonacci and Lucas numbers have been obtained by using generalized Fibonacci numbers. In addition, some new properties of generalized Fibonacci...

Lucas number | Generalized Fibonacci number | Binomial coefficients | Fibonacci number | MATHEMATICS, APPLIED

Lucas number | Generalized Fibonacci number | Binomial coefficients | Fibonacci number | MATHEMATICS, APPLIED

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 04/2019, Volume 69, Issue 2, pp. 327 - 338

Sums of products of two Gaussian -binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight...

Primary 11B39 | Secondary 05A30 | binomial coefficients | Fibonomial and Lucanomial coefficients | sums identites | partial fraction decomposition | Gaussian | Gaussian q-binomial coefficients | MATHEMATICS | GENERALIZED FIBONACCI | IDENTITIES | FIBONOMIAL SUMS

Primary 11B39 | Secondary 05A30 | binomial coefficients | Fibonomial and Lucanomial coefficients | sums identites | partial fraction decomposition | Gaussian | Gaussian q-binomial coefficients | MATHEMATICS | GENERALIZED FIBONACCI | IDENTITIES | FIBONOMIAL SUMS

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 5/2014, Volume 34, Issue 1, pp. 143 - 156

Let t be a fixed parameter and x some indeterminate. We give some properties of the generalized binomial coefficients $\genfrac{\langle...

Generalized binomial coefficients | Fourier Analysis | Functions of a Complex Variable | 05A10 | Field Theory and Polynomials | 11B65 | Mathematics | Number Theory | Combinatorics | MATHEMATICS | PROOFS | IDENTITIES

Generalized binomial coefficients | Fourier Analysis | Functions of a Complex Variable | 05A10 | Field Theory and Polynomials | 11B65 | Mathematics | Number Theory | Combinatorics | MATHEMATICS | PROOFS | IDENTITIES

Journal Article

Journal of Integer Sequences, 2015, Volume 18, Issue 5

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 11

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range...

generalized hypergeometric function | generalized harmonic numbers | Mathematics | harmonic numbers | polygamma functions | Hurwitz zeta function | Stirling numbers of the first kind | summation formulas for | psi-function | Analysis | Riemann zeta function | Mathematics, general | Applications of Mathematics | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Psi-function | Summation formulas for | Generalized hypergeometric function | MATHEMATICS, APPLIED | generalized hypergeometric function F-p(q) | MATHEMATICS | ZETA | summation formulas for F-p(q) | SERIES REPRESENTATIONS | Harmonics | Operators | Algorithms | Binomial coefficients | Mathematical analysis | Elementary particles | Inequalities | Series (mathematics)

generalized hypergeometric function | generalized harmonic numbers | Mathematics | harmonic numbers | polygamma functions | Hurwitz zeta function | Stirling numbers of the first kind | summation formulas for | psi-function | Analysis | Riemann zeta function | Mathematics, general | Applications of Mathematics | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Psi-function | Summation formulas for | Generalized hypergeometric function | MATHEMATICS, APPLIED | generalized hypergeometric function F-p(q) | MATHEMATICS | ZETA | summation formulas for F-p(q) | SERIES REPRESENTATIONS | Harmonics | Operators | Algorithms | Binomial coefficients | Mathematical analysis | Elementary particles | Inequalities | Series (mathematics)

Journal Article

6.
Full Text
Generalized Levinson–Durbin sequences, binomial coefficients and autoregressive estimation

Journal of Multivariate Analysis, ISSN 0047-259X, 2010, Volume 101, Issue 5, pp. 1263 - 1273

For a discrete time second-order stationary process, the Levinson–Durbin recursion is used to determine the coefficients of the best linear predictor of the...

Generalized Levinson–Durbin sequence | Least squares estimator | Binomial coefficients | Levinson–Durbin sequence | Partial correlations | Yule–Walker estimator | Generalized Levinson-Durbin sequence | Yule-Walker estimator | Levinson-Durbin sequence | MAXIMUM-LIKELIHOOD | BIAS | TIME-SERIES | STATISTICS & PROBABILITY | PREDICTION | Binomial coefficients Generalized Levinson-Durbin sequence Least squares estimator Levinson-Durbin sequence Partial correlations Yule-Walker estimator

Generalized Levinson–Durbin sequence | Least squares estimator | Binomial coefficients | Levinson–Durbin sequence | Partial correlations | Yule–Walker estimator | Generalized Levinson-Durbin sequence | Yule-Walker estimator | Levinson-Durbin sequence | MAXIMUM-LIKELIHOOD | BIAS | TIME-SERIES | STATISTICS & PROBABILITY | PREDICTION | Binomial coefficients Generalized Levinson-Durbin sequence Least squares estimator Levinson-Durbin sequence Partial correlations Yule-Walker estimator

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2014, Volume 3, Issue 1, pp. 1 - 7

The Intraclass Correlation Coefficient (ICC) is commonly used to estimate the similarity between quantitative measures obtained from different sources....

Negative binomial mixed model | Intraclass correlation coefficient | Variance components | Generalized linear mixed model | Science, general | MODELS | MULTIDISCIPLINARY SCIENCES

Negative binomial mixed model | Intraclass correlation coefficient | Variance components | Generalized linear mixed model | Science, general | MODELS | MULTIDISCIPLINARY SCIENCES

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2197 - 2202

We obtain explicit formulas that express the complete homogeneous symmetric polynomials of the sequence of partial sums sk of a sequence xk as polynomials in...

Legendre–Stirling numbers | Symmetric polynomials | Gaussian coefficients | Generalized Stirling numbers | [formula omitted]-Stirling numbers | q-Stirling numbers | Legendre-Stirling numbers | MATHEMATICS | DIVIDED DIFFERENCES | PASCAL MATRICES

Legendre–Stirling numbers | Symmetric polynomials | Gaussian coefficients | Generalized Stirling numbers | [formula omitted]-Stirling numbers | q-Stirling numbers | Legendre-Stirling numbers | MATHEMATICS | DIVIDED DIFFERENCES | PASCAL MATRICES

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 01/2014, Volume 21, Issue 1

We work with a generalization of Stirling numbers of the second kind related to the boson normal ordering problem (P. Blasiak et al.). We show that these...

Powers of binomial coefficients | Generalized stirling numbers | MATHEMATICS | MATHEMATICS, APPLIED | generalized Stirling numbers | powers of binomial coefficients

Powers of binomial coefficients | Generalized stirling numbers | MATHEMATICS | MATHEMATICS, APPLIED | generalized Stirling numbers | powers of binomial coefficients

Journal Article

Journal of Number Theory, ISSN 0022-314X, 10/2014, Volume 143, pp. 293 - 319

For any positive integer n and variables a and x we define the generalized Legendre polynomial Pn(a,x) by Pn(a,x)=∑k=0n(ak)(−1−ak)(1−x2)k. Let p be an odd...

Generalized Legendre polynomial | Binomial coefficient | Congruence | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | SUMS

Generalized Legendre polynomial | Binomial coefficient | Congruence | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | SUMS

Journal Article

Integers, ISSN 1867-0652, 06/2009, Volume 9, Issue 2, pp. 167 - 175

The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete...

partial autocorrelations | Binomial coefficients | Levinson–Durbin–Whittle sequence | Levinson–Durbin sequence | stationary process | generalized Levinson–Durbin sequence

partial autocorrelations | Binomial coefficients | Levinson–Durbin–Whittle sequence | Levinson–Durbin sequence | stationary process | generalized Levinson–Durbin sequence

Journal Article

Advances in Applied Mathematics, ISSN 0196-8858, 2010, Volume 45, Issue 4, pp. 564 - 606

The following topics and their interconnection are discussed: 1. a general product inequality for the weighted seminorms on the vector space of formal power...

Binomial coefficients | Univalent functions | Weighted inequalities for sums | Laplace–Borel transforms | Exponentiation | Gamma and beta functions | Binomial inequalities | Bernstein polynomials | Generalized hypergeometric series | Weighted norm inequalities | Entire functions | Seminorms for formal power series | Convolutions | Laplace-Borel transforms | GAMMA | MATHEMATICS, APPLIED | BIEBERBACH CONJECTURE | POWER-SERIES | THEOREMS | Interconnection | Mathematical analysis | Transforms | Inequalities | Images | Norms | Binomials

Binomial coefficients | Univalent functions | Weighted inequalities for sums | Laplace–Borel transforms | Exponentiation | Gamma and beta functions | Binomial inequalities | Bernstein polynomials | Generalized hypergeometric series | Weighted norm inequalities | Entire functions | Seminorms for formal power series | Convolutions | Laplace-Borel transforms | GAMMA | MATHEMATICS, APPLIED | BIEBERBACH CONJECTURE | POWER-SERIES | THEOREMS | Interconnection | Mathematical analysis | Transforms | Inequalities | Images | Norms | Binomials

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 02/2019, Volume 758, pp. 42 - 60

We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of...

Binomial coefficients of words | Bertrand numeration systems | Generalized Pascal triangles | Parry numbers | Perron numbers | β-expansions | COEFFICIENTS | COMPUTER SCIENCE, THEORY & METHODS | beta-expansions

Binomial coefficients of words | Bertrand numeration systems | Generalized Pascal triangles | Parry numbers | Perron numbers | β-expansions | COEFFICIENTS | COMPUTER SCIENCE, THEORY & METHODS | beta-expansions

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 06/2018, Volume 67, pp. 71 - 77

In this paper we present theoretical and computational results regarding generalized arithmetic m-triangles. The numerical values recover well-known number...

asympotic formulae | pentanomial numbers | generalized binomial coefficients | recurrent sequences

asympotic formulae | pentanomial numbers | generalized binomial coefficients | recurrent sequences

Journal Article

Statistics in Medicine, ISSN 0277-6715, 03/2017, Volume 36, Issue 6, pp. 1029 - 1040

Longitudinal binomial data are frequently generated from multiple questionnaires and assessments in various scientific settings for which the binomial data are...

beta‐binomial model | generalized linear mixed‐effects model | generalized estimating equation | overdispersion | probit model | generalized linear mixed-effects model | beta-binomial model | MEDICINE, RESEARCH & EXPERIMENTAL | MEDICAL INFORMATICS | STATISTICS & PROBABILITY | PREMANIFEST | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | MATHEMATICAL & COMPUTATIONAL BIOLOGY | HUNTINGTONS-DISEASE | PROGRESSION | Binomial Distribution | Data Interpretation, Statistical | Huntington Disease - epidemiology | Algorithms | Humans | Risk Factors | Linear Models | Models, Statistical | Prodromal Symptoms | Longitudinal Studies | Usage | Models | Huntington's chorea | Analysis

beta‐binomial model | generalized linear mixed‐effects model | generalized estimating equation | overdispersion | probit model | generalized linear mixed-effects model | beta-binomial model | MEDICINE, RESEARCH & EXPERIMENTAL | MEDICAL INFORMATICS | STATISTICS & PROBABILITY | PREMANIFEST | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | MATHEMATICAL & COMPUTATIONAL BIOLOGY | HUNTINGTONS-DISEASE | PROGRESSION | Binomial Distribution | Data Interpretation, Statistical | Huntington Disease - epidemiology | Algorithms | Humans | Risk Factors | Linear Models | Models, Statistical | Prodromal Symptoms | Longitudinal Studies | Usage | Models | Huntington's chorea | Analysis

Journal Article

16.
Multivariate meixner, charlier and krawtchouk polynomials according to analysis on symmetric cones

Journal of Lie Theory, ISSN 0949-5932, 2016, Volume 26, Issue 2, pp. 439 - 477

We introduce some multivariate analogues of Meixner, Charlier and Krawtchouk polynomials, and establish their main properties by using analysis on symmetric...

Symmetric cones | Spherical polynomials | Generalized binomial coeffcients | Multivariate analysis | Discrete orthogonal polynomials | MATHEMATICS | spherical polynomials | symmetric cones | generalized binomial coefficients | discrete orthogonal polynomials

Symmetric cones | Spherical polynomials | Generalized binomial coeffcients | Multivariate analysis | Discrete orthogonal polynomials | MATHEMATICS | spherical polynomials | symmetric cones | generalized binomial coefficients | discrete orthogonal polynomials

Journal Article

Journal of Statistical Computation and Simulation, ISSN 0094-9655, 03/2019, Volume 89, Issue 4, pp. 615 - 640

In order to combat multicollinearity, the r - d class estimator was introduced in linear and binary logistic regression models. Since the generalized linear...

principal component regression estimator | maximum likelihood estimator | mean squared error | Liu estimator | Generalized linear models | RIDGE-REGRESSION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PRINCIPAL COMPONENT REGRESSION | STATISTICS & PROBABILITY | LIU-TYPE ESTIMATOR | SIMULATION | Regression coefficients | Regression models | Statistical analysis | Statistical models | Approximation | Computer simulation | Poisson density functions | Shrinkage | Regression analysis | Iterative methods | Estimators

principal component regression estimator | maximum likelihood estimator | mean squared error | Liu estimator | Generalized linear models | RIDGE-REGRESSION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PRINCIPAL COMPONENT REGRESSION | STATISTICS & PROBABILITY | LIU-TYPE ESTIMATOR | SIMULATION | Regression coefficients | Regression models | Statistical analysis | Statistical models | Approximation | Computer simulation | Poisson density functions | Shrinkage | Regression analysis | Iterative methods | Estimators

Journal Article

Biometrika, ISSN 0006-3444, 9/2009, Volume 96, Issue 3, pp. 735 - 749

We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function....

Generalized linear model | Time series models | Time series | Polio | Standard error | Standard deviation | Regression analysis | Binomials | Parametric models | Estimators | Time series of counts | Latent process | Negative binomial distribution | STATE-SPACE MODELS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STATISTICS & PROBABILITY | REGRESSION-MODEL | Studies | Binomial distribution | Generalized linear models

Generalized linear model | Time series models | Time series | Polio | Standard error | Standard deviation | Regression analysis | Binomials | Parametric models | Estimators | Time series of counts | Latent process | Negative binomial distribution | STATE-SPACE MODELS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STATISTICS & PROBABILITY | REGRESSION-MODEL | Studies | Binomial distribution | Generalized linear models

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2017, Volume 86, Issue 304, pp. 899 - 933

We define a Gauss factorial N_n! to be the product of all positive integers up to N that are relatively prime to n\in \mathbb{N}. In this paper we study...

Generalized Fermat numbers | Congruences | Gauss-Wilson theorem | Gauss factorials | Binomial coefficient congruences | Factors | MATHEMATICS, APPLIED | generalized Fermat numbers | congruences | GAUSS | MULTIPLICATIVE ORDERS | binomial coefficient congruences | factors

Generalized Fermat numbers | Congruences | Gauss-Wilson theorem | Gauss factorials | Binomial coefficient congruences | Factors | MATHEMATICS, APPLIED | generalized Fermat numbers | congruences | GAUSS | MULTIPLICATIVE ORDERS | binomial coefficient congruences | factors

Journal Article

Fisheries Research, ISSN 0165-7836, 2007, Volume 84, Issue 2, pp. 210 - 221

The zero-inflated negative binomial (ZINB) regression model with smoothing is introduced for modeling count data with many zero-valued observations, and its...

Spline smoothing | CPUE | GAM | Zero-inflated | Shark | Negative binomial | GLM | EM algorithm | shark | STANDARDIZATION | spline smoothing | PELAGIC SHARKS | GENERALIZED LINEAR-MODELS | FISHERY | CATCH RATES | FISHERIES | ABUNDANCE DATA | negative binomial | POISSON REGRESSION | zero-inflated | SELECTION | LIKELIHOOD | INDEXES | Analysis | Models | Algorithms

Spline smoothing | CPUE | GAM | Zero-inflated | Shark | Negative binomial | GLM | EM algorithm | shark | STANDARDIZATION | spline smoothing | PELAGIC SHARKS | GENERALIZED LINEAR-MODELS | FISHERY | CATCH RATES | FISHERIES | ABUNDANCE DATA | negative binomial | POISSON REGRESSION | zero-inflated | SELECTION | LIKELIHOOD | INDEXES | Analysis | Models | Algorithms

Journal Article

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