As a hybrid of N-gram in natural language processing and collocation in statistical linguistics, multi-word is becoming a hot topic in area of text mining and information retrieval. In this paper, a study concerning distribution of multi-words is carried out to explore a theoretical basis for probabilistic term-weighting scheme. Specifically, the Poisson distribution, zero-inflated binomial dis...

We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing has been well studied, none of the existing approaches takes transaction cos...

Binomial trees are widely used for both financial and real option pricing due to their ease of use, versatility and precision. However, the classic approach developed by Cox, Ross, and Rubinstein (1979) applies only to a Geometric Brownian Motion diffusion processes, limiting the modeling choices. Nelson and Ramaswamy (1990) provided a general method to construct recombining binomial lattices w...

Good control charts for high quality processes are often based on the number of successes between failures. Geometric charts are simplest in this respect, but slow in recognizing moderately increased failure rates p. Improvement can be achieved by waiting until r > 1 failures have occurred, i.e. by using negative binomial charts. In this paper we analyze such charts in some detail. On the basis...

Negative binomial and Poisson processes {X(t), t ≥ 0} have cumulants proportional to the rate λ. So, formal Cornish-Fisher expansions in powers of λ−1/2 are available for their cumulative distribution function and quantiles. If T is an independent random variable with cumulants proportional to γ then the cumulants of X(T ) are proportional to γ; so, CornishFisher expansions in powers of γ−1/2 a...

For processes concerning attribute data with (very) small failure rate p, often negative binomial control charts are used. The decision whether to stop or continue is made each time r failures have occurred, for some r ≥ 1. Finding the optimal r for detecting a given increase of p first requires alignment of the charts in terms of in-control behavior. In the present paper binomial charts are su...