Results 71 to 80 of about 96,717 (274)
Explicit constants in the nonuniform local limit theorem for Poisson binomial random variables
Journal of Inequalities and ApplicationsIn a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P ( S = k ) $P(S=k)$ when S = ∑ i = 1 n X i $S=\sum_{i=1}^{n}X_{i}$ and X 1 , X 2 , … , X n $X_{1},X_{2},\ldots ,X_{n}$ are ...
Graeme Auld, Kritsana Neammanee
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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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Journal of Time Series Analysis, EarlyView.This article reviews and compares popular methods, some old and some recent, that produce time series having Poisson marginal distributions. The article begins by narrating ways where time series with Poisson marginal distributions can be produced.
Jiajie Kong, Robert Lund
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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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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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Acta Physica Sinica, 2013 We propose an operator Hermite polynomial method, namely, we replace the arguments of the special function by quantum mechanical operators, and in this way we derive a binomial theorem involving Hermite polynomials and a negative-binomial theorem involving Laguerre polynomials.
null Fan Hong-Yi +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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Markov Determinantal Point Process for Dynamic Random Sets
Journal of Time Series Analysis, EarlyView.ABSTRACT The Law of Determinantal Point Process (LDPP) is a flexible parametric family of distributions over random sets defined on a finite state space, or equivalently over multivariate binary variables. The aim of this paper is to introduce Markov processes of random sets within the LDPP framework. We show that, when the pairwise distribution of two
Christian Gouriéroux, Yang Lu
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Tests for Changes in Count Time Series Models With Exogenous Covariates
Journal of Time Series Analysis, EarlyView.ABSTRACT We deal with a parametric change in models for count time series with exogenous covariates specified via the conditional distribution, i.e., with integer generalized autoregressive conditional heteroscedastic models with covariates (INGARCH‐X).
Šárka Hudecová, Marie Hušková
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Polynomials of binomial type and Lucas’ Theorem [PDF]
Proceedings of the American Mathematical Society, 2015 At the intersection of number theory, commutative algebra and combinatorics. The new version has additional references.
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