We introduce a family of q-analogues of the binomial distribution, which generalises the Stieltjes-Wigert-, Rogers-Szegö-, and Kemp-distribution. Basic properties of this familiy are provided and several convergence results involving the classical binomial, Poisson, discrete normal distribution, and a family of q-analogues of the Poisson distribution are established. These results generalise co...

We show that the inverse moments of a binomial random variable are such that

Individuals may join groups for several reasons, one of which is the possibility of sharing information about the quality of a foraging area. Sharing information in a patch-foraging scenario gives each group member an opportunity to make a more accurate estimate of the quality of the patch. In this paper we present a mathematical model in which we study the effect of group size on patch-leaving...

In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...

This is a good place to point out that these are only (approximating) , and not full truth. models Truth is not a model. A model, by definition, is an approximation (and not truth). In fact, out of a few million coin flips, one or more coins will remain standing on edge – that is truth. The binomial model does not allow such reality. The idea is more easily understood for the outcomes “dead" or...