In this article, we study the applicability of Benford’s law and Zipf’s law to national COVID-19 case figures with the aim of establishing guidelines upon which methods of fraud detection in epidemiology, based on formal statistical analysis, can be developed. Moreover, these approaches may also be used in evaluating the performance of public health surveillance systems. We provide theoretical arguments for why the empirical laws should hold in the early stages of an epidemic, along with preliminary empirical evidence in support of these claims. Based on data published by the World Health Organization and various national governments, we find empirical evidence that suggests that both Benford’s law and Zipf’s law largely hold across countries, and deviations can be readily explained. To the best of our knowledge, this paper is among the first to present a practical application of Zipf’s law to fraud detection.

We propose a model to assess the value of a distributor in a dynamic stochastic cooperative advertising supply chain in which a manufacturer wholesales its product to a distributor who in turn sells it to a retailer. Moreover and importantly, the distributor also intermediates the pricing and advertising decisions between the manufacturer and the retailer. For the resulting three‐player hierarchical game formulation of the supply chain, we characterize the feedback Stackelberg equilibrium in terms of a system of coupled algebraic equations and show it to admit a unique solution. We find that the value added by the distributor to the supply chain depends critically on the nature of the demand function for the product, a result that has practical implications for the kinds of product where having a distributor is most desirable. Second, our model indicates that the presence of the distributor can enhance the margins of both the retailer and the manufacturer relative to the case of no distributor, and provide explicit conditions for this to occur. Third, we present numerical analysis that indicates that if the distributor generates sufficiently large transportation cost savings, then the three‐echelon supply chain can lead in the long run to higher market awareness, lower advertising expenditure, and higher value extracted, relative to the two‐echelon model. Finally, in addition to retailer advertising that is subsidized by the manufacturer, we also provide the manufacturer an option to do national advertising and show its viability.

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<p>This thesis investigates the stochastic properties of high frequency foreign exchange data. We study the exchange rate as a process driven by Brownian motion, paying particular attention to its sampled total variation, along with the variance and distribution of its increments. The normality of its increments is tested using the Khmaladze transformation-2, which we show is straightforward to implement for the case of testing centred normality. We found that while the process exhibits properties characteristic of Brownian motion, increments are non-Gaussian and instead come from mixture distributions. We also introduce a technical analysis trading strategy for predicting price movements, and employ it using the exchange rate dataset. This strategy is shown to offer a statistically significant advantage, and provides evidence that exchanges rates are predictable to a greater extent than current mathematical models suggest.</p>