Although the kurtosis index proposed by Karl Pearson in 1905 is introduced in statistical textbooks at all levels, the measure is not easily interpreted and has been a subject of considerable debate. In this study, the theoretical development of kurtosis is surveyed from a historical perspective of Pearson's work on evolution. It surprisingly emerges that there was no emphasis in Pearson's papers on kurtosis as measuring (in part) tail heaviness. However, it is found that Pearson used to frequently adjust the formalisation of kurtosis depending on his changing needs. This complex development partly explains the confusion that would surround kurtosis in subsequent literature. Our conclusion is that most misunderstandings arise from improper use of the kurtosis coefficient outside the Pearson system of frequency curves. Copyright (c) 2009 The Authors. Journal compilation (c) 2009 International Statistical Institute.

In many tourism destinations, sustainability of the local economy leans on small and medium-sized hotels that are individually owned and operated by members of the community. Suffering from seasonality more than their big competitors, these hotels should undertake marketing initiatives to counteract wide demand fluctuations. Such initiatives are most effective if based on accurate occupancy forecasts, which must be performed at the individual hotel level. In this aim, the present paper suggests a demand forecasting approach adapted to specific features that characterize reservation data for small and medium-sized enterprises (SMEs) in the hospitality sector. The proposed framework integrates historical and advanced booking methods into a forecast combination with time-varying, performance-based weights. Whereas historical methods use only past observations about the number of guests recorded on a particular stay night to forecast future room occupancy (long-term perspective), advanced booking methods predict bookings-to-come based on partially accumulated data from reservations on hand (short-term perspective). In order to provide a possible solution to data sparsity issues that affect the application of advanced booking models to hospitality SMEs, a procedure that incorporates length-of-stay information directly into the reservation processing phase is also introduced. The methodology is tested on real time series of reservation data from three Italian hotels, located either in a city center (Milan) or in a typical destination for seasonal holidays (Lake Maggiore). Model parameters are calibrated on a training dataset and the accuracy of the occupancy forecasts is evaluated on a holdout sample. The results validate earlier findings about combinations of long-term and short-term forecasts and, in addition, show that using performance-based weights improves the quality of forecasts. Reducing the risk of large forecast failures, the proposed methodology can indeed have practical implications for the design and implementation of effective demand-side policies in hospitality SMEs. These policies are expected to provide a competitive advantage that can be crucial to the sustainability of small establishments in a context of growing global tourism.

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Abstract:In this paper we analyze insurance demand when the utility function depends both upon final wealth and the level of losses or gains relative to a reference point. Besides some comparative statics results, we discuss the links with first-order risk aversion, with the Omega measure, and with a tendency to over-insure modest risks that has been been extensively documented in real insurance markets.