Generating functions for generalized binomial distributions

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties: the constraints of nonnegativeness are automatically fulfilled, a complete characterization in terms of generating functions is given and a large number of analytical examples becomes available.Comment: PDFLaTex, 27 pages, 5 figure

On a generalization of the binomial distribution and its Poisson-like limit

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We discuss under which conditions this distribution can have a probabilistic interpretation.Comment: 17 pages, 6 figure

2,4,5-Tris(biphenyl-2-yl)-1-bromo­benzene

In the title compound, C42H29Br, the dihedral angles between the central benzene ring and the three attached benzene rings are very similar, lying in the range 52.65 (6)–57.20 (7)°. Of the dihedral angles between the rings of the o-biphenyl substituents, two are similar [46.34 (7) and 47.35 (7)°], while the other differs significantly [64.17 (7)°]. In the crystal, mol­ecules are linked into centrosymmetric dimers by two weak C—H⋯π inter­actions