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Volume 31 - Issue 2 - December 2006
David Chappell and Su Zhang
This paper proposes a theoretical model of the political business cycle. The model is used to test for the existence of a political business cycle in Germany during Chancellor Schroeder's first term in office (October 1998 to September 2002). We find some evidence to support the presence of a political business cycle.
Qingzhi Yao and Yuyuan Zhao
This short article describes a probabilistic model for analysing the numbers of namesakes (i.e. persons with identical names) in a population. The model is applied to the Chinese population, which has an extremely high number of namesakes. A practical measure to reduce the numbers of namesakes is proposed.
Sérgio B. Volchan
In this paper we present one of the main results of collective risk theory in non-life insurance mathematics, which says that for small claims the ruin probability decreases exponentially fast. The discussion is made in the context of the classical Cramér–Lundberg model using the martingale technique.
B. D. Puza and T. J. O'Neill
A methodology is proposed for dealing with selection bias in volunteer surveys where the data are binary. Use is made of an assumed relationship between the probabilities of inclusion in samples for yes-responses and no-responses, and it is shown how statements about this relationship may be justified. Bayesian techniques aided by Markov chain Monte Carlo methods are employed for incorporating prior information and uncertainty into the inferential process. A design-based approach is also considered. The theory is applied to some Australian public opinion poll data.
Jonathan J. Shuster, Samuel S. Wu and Anqi Sun
This article will look at a variety of 4-team tournaments under various alternatives of seeding the teams and play progression. Measures of evaluation include the severity of the penalty for early losses, the average number of games played (and played by the winner), the probability that the best team wins, the average quality of the winner, and the standard deviations of the latter two quantities under random seeding. The current double-elimination format used in US Men's Baseball and Women's Softball is highly concordant with a single-elimination tournament, and overly penalizes early losses. A new design is recommended to replace the current tournament design. In addition, we have found an alternate to best-of-three elimination tournaments that has superior properties under similar average number of games played.
An unbiased Markov random walk with catastrophes, in continuous time, was introduced by Switkes (2004), who ascertained the transient and equilibrium behaviour of the walk, and proposed several open problems for this and related processes. Here we consider several examples of continuous-time Markov chains in the presence of catastrophes, and address similar questions. We also consider the properties of first passage times of these processes. Our results resolve a number of the open problems proposed by Switkes (2004).
Flora A. Mulkey and Randall Swift
In this paper, we consider a birth–death process with the Allee effect. This process is a generalization of the logistic birth–death process considered by Swift (2001). We review the relationship between the Allee effect and the extensively studied logistic model, and we present a stochastic formulation. We analyse the stochastic model and make a comparison with its deterministic counterpart. Finally, we analyse a birth–death–immigration–emigration model with the Allee effect.