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...

An approximate formula for pricing American options along the lines of MacMillan [1986] and Barone-Adesi and Whaley [1987] is presented. This analytical approximation is as efficient as the existing ones, but it is remarkably more accurate. In particular, it yields good results for long maturity options for which the existing analytical ones fare poorly. It is also demonstrated that this approx...

Introduction The One-Sample Proportion Test is used to assess whether a population proportion (P1) is significantly different from a hypothesized value (P0). This is called the hypothesis of inequality. The hypotheses may be stated in terms of the proportions, their difference, their ratio, or their odds ratio, but all four hypotheses result in the same test statistics. For example, suppose tha...

We discuss the identification of features that are associated with an outcome in RNA-Sequencing (RNA-Seq) and other sequencing-based comparative genomic experiments. RNA-Seq data takes the form of counts, so models based on the normal distribution are generally unsuitable. The problem is especially challenging because different sequencing experiments may generate quite different total numbers o...

Most multicast algorithms proposed in the literature assume an arbitrarily long message being communicated as a single packet. Modern networks typically limit the size of the largest packet, and long messages are packetized and transmitted. Such networks also provide network interface support for nodes, which typically includes a coprocessor and memory, to implement the lower layers of the comm...

SUMMARY To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has cover...

In cross-sectional or cohort studies with binary outcomes, it is biologically interpretable and of interest to estimate the relative risk or prevalence ratio, especially when the response rates are not rare. Several methods have been used to estimate the relative risk, among which the log-binomial models yield the maximum likelihood estimate (MLE) of the parameters. Because of restrictions on t...

This paper proves an identity between flagged Schur polynomials, giving a duality row flags and column flags. generalises both the binomial determinant theorem due to Gessel Viennot symmetric function Aitken. As corollaries we obtain lifts of \(q\)-binomial coefficients polynomials. Our method is path counting argument on novel lattice generalising that used by Viennot.

I present a new algorithm for computing binomial coefficients modulo 2N. The proposed method has an O(N3·Multiplication(N)+N4) preprocessing time, after which a binomial coefficient C(P, Q) with 0≤Q≤P≤2N-1 can be computed modulo 2N in O(N2·log(N)·Multiplication(N)) time. Multiplication(N) denotes the time complexity of multiplying two N-bit numbers, which can range from O(N2) to O(N·log(N)·log(...