We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately repr...

Modern networks typically limit the size of the largest packet for efficient communication. Thus, 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 communication protocol. This paper presents a concept of smart network interface support for packetiz...

A new multiplicity distribution with multifractal properties which can be used in high-energy physics and quantum optics is proposed. It may be considered as a generalization of the negative-binomial distribution. We find the structure of the generating function for such distribution and discuss its properties.

In a variety of research domains, data are generated as a consequence of the count process and may possess an ‘excess’ of zeros. There have been many attempts to analyse such data using different statistical methods, including the zero-inflated Poisson (ZiP) and zero-inflated binomial (ZiB) models. The interpretation of these models is however problematic if the covariates considered for the no...

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

The generalized additive model is extended to handle negative binomial responses. The extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family. The methodology is applied to data involving DNA adduct counts and smoking variables among ex-smokers with lung cancer. A more detailed investigation is made of the parametric r...

Usual approaches for estimating the variance of a standardized rate may not be applicable to rates of recurrent events. Where individuals are prone to repeated health events, Greenwood and Yule (J R Stat Soc [A], 1920;83:255-79) advocated use of the negative binomial distribution to account for departures from the assumption of randomness of recurrent events required by the Poisson distribution...

Binomial trees have been used extensively for broadcasting in clusters of workstations. In the case of heterogeneous nondedicated clusters and grid environments, the broadcasting occurs over a heterogeneous network, and the performance obtained by the broadcast algorithm will depend on the organization of the nodes onto the binomial tree. The organization of the nodes should take into account t...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are respectively first, second and third order approximations w.r.t. th...