Implied binomial trees are constructed by fitting a risk-neutral density (in the form of ending nodal probabilities) to observed option prices. Since there are usually not enough options traded in the marketplace, a quadratic program is often used to extract the ending nodal probabilities from observed option prices. A problem with this commonly used approach is that the quadratic program is us...

For several pairs (P,Q) of classical distributions on N0, we show that their stochastic ordering P ≤st Q can be characterized by their extreme tail ordering equivalent to P ({k∗})/Q({k∗}) ≤ 1 ≤ limk→k∗ P ({k})/Q({k}), with k∗ and k∗ denoting the minimum and the supremum of the support of P + Q, and with the limit to be read as P ({k∗})/Q({k∗}) for k∗ finite. This includes in particular all pair...

Biometric Identification Devices (BID’s) compare a physiological measurement of an individual to a database of stored templates. The goal of any BID is to correctly match those two quantities. When the comparison between the measurement and the template is performed the result is either an ”accept” or a ”reject.” For a variety of reasons, errors occur in this process. Consequently, false reject...

BACKGROUND Reporting of absolute risk difference (RD) is recommended for clinical and epidemiological prospective studies. In analyses of multicenter studies, adjustment for center is necessary when randomization is stratified by center or when there is large variation in patients outcomes across centers. While regression methods are used to estimate RD adjusted for baseline predictors and clus...

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...