Results 81 to 90 of about 94,783 (262)
From Classical to Modern Nonlinear Central Limit Theorems
MathematicsIn 1733, de Moivre, investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theorem (CLT).
Vladimir V. Ulyanov
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Binomial Theorem based on Annamalai's Binomial Identity
, 2022 This paper presents a binomial theorem and proof based on Annamalai’s binomial identity. The factorial function defined for non-negative integers, denoted by n!, is the product of all positive integers less than or equal to n. This theorem uses the factorial function and Annamalai’s binomial identity.
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Fractional Sums and Differences with Binomial Coefficients
Discrete Dynamics in Nature and Society, 2013 In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad +3 more
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On Exponential‐Family INGARCH Models
Journal of Time Series Analysis, EarlyView.ABSTRACT A range of integer‐valued generalised autoregressive conditional heteroscedastic (INGARCH) models have been proposed in the literature, including those based on conditional Poisson, negative binomial and Conway‐Maxwell‐Poisson distributions. This note considers a larger class of exponential‐family INGARCH models, showing that maximum empirical
Alan Huang +3 more
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On Binomial Identities in Arbitrary Bases
, 2016 We extend the digital binomial identity as given by Nguyen el al. to an identity in an arbitrary base $b$, by introducing the $b-$ary binomial coefficients.
Jiu, Lin, Vignat, Christophe
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Time‐Varying Dispersion Integer‐Valued GARCH Models
Journal of Time Series Analysis, EarlyView.ABSTRACT We introduce a general class of INteger‐valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing simultaneously time‐varying mean and dispersion parameters. We call such models time‐varying dispersion INGARCH (tv‐DINGARCH) models.
Wagner Barreto‐Souza +3 more
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Distribution of the combinatorial multisets component vectors
Lietuvos Matematikos Rinkinys, 2012 We explore a class of random combinatorial structures called weighted multisets. Their components are taken from an initial set satisfying general boundedness conditions posed on the number of elements with a given weight.
Eugenijus Manstavičius +1 more
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A nonuniform local limit theorem for Poisson binomial random variables via Stein’s method
Journal of Inequalities and ApplicationsWe prove a nonuniform local limit theorem concerning approximation of the point probabilities P ( S = k ) $P(S=k)$ , where S = ∑ i = 1 n X i $S=\sum_{i=1}^{n}X_{i}$ , and X 1 , … , X n $X_{1},\ldots ,X_{n}$ are independent Bernoulli random variables with
Graeme Auld, Kritsana Neammanee
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Developing coral seeding devices and rapid deployment methods to scale up reef restoration
Restoration Ecology, EarlyView.Current coral restoration methods are constrained by several factors, including low survival rates and high costs of coral production and deployment, making it difficult to address ecosystem‐wide coral declines. This study introduces a new two‐part coral seeding concept to efficiently settle, transport, and deploy coral spat.
Blake D. Ramsby +7 more
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A proper concordance index for models with crossing hazards
Scandinavian Journal of Statistics, EarlyView.Abstract Concordance indices are among the most popular metrics used for model selection and evaluation in survival analysis. This is due to their clear interpretation and these metrics being proper for survival models where hazards cannot cross, such as proportional hazards models.
A. Gandy, T. J. Matcham
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