Search results for "Binomial approximation"
showing 3 items of 3 documents
Approximation Operators of Binomial Type
1999
Our objective is to present a unified theory of the approximation operators of binomial type by exploiting the main technique of the so- called “ umbral calculus” or “finite operator calculus” (see [18], [20]-[22]). Let us consider the basic sequence (bn)n≥0 associated to a certain delta operator Q. By supposing that b n (x) ≥ 0, x ∈ [0, ∞), our purpose is to put in evidence some approximation properties of the linear positive operators (L Q n ) n≥1 which are defined on C[0,1] by \( L_n^Qf = \sum\limits_{k = 0}^n {\beta _n^Q{,_k}f\left( {\frac{k}{n}} \right),\beta _{n{,_k}}^Q\left( x \right): = } \frac{1}{{{b_n}\left( n \right)}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right){b_…
A generalization of the Binomial distribution based on the dependence ratio
2014
We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper–Haseman's Cor…
Correspondence between generalized binomial field states and coherent atomic states
2008
We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.