<p> We study the problem of finding approximate significance points of random variables whose exact distributions are unknown or extremely complicated . We consider the case where at least the first three moments, and possibly the lower or upper endpoint of the distribution are known. </p> <p> The methods of approximation studied include the Johnson system of transformations, Pearson curves, Pearson curves with known lower terminal, Cornish-Fisher expansions and the approximation a+bW, where W is chi-squared with p degrees of freedom . A new three-moment approximation of the form (cW)^k, with W as defined above, is also considered. These methods of approximation are discussed, with special attention to fitting procedures and computer implementation. </p> <p> The methods of approximation are compared, with respect to ease of application and accuracy of approximation, over a wide variety of exact distributions. The accuracy of each approximation is discussed and guidelines are given for determining which of several approximations should be used in a particular case. </p> / Thesis / Master of Science (MSc)

This study examines poor travellers who were on the move during the seventeenth and eighteenth centuries. The focus is the County of Devon, with Exeter dealt with only briefly as it was a separate county. It is shown that the travellers, including numbers of Irish in the seventeenth century and foreign-born, particularly in the eighteenth century, were affected by a number of factors, but that the most important influence on their numbers and types was the incidence of wars. Economic factors, such as food supply, were of some importance, but the economy too was influenced by the effects of wars. Legislation also was found to have had less influence than expected. However, the legislation effective from 1700 did have a marked impact on the documentation available. The main sources used for this study are the parochial documents provided by churchwardens’ accounts of payments made to travellers in need and some of those of the parish overseers. These are supplemented by the records of Devon’s County Quarter Sessions. A combination of Devon’s geography, its strong international maritime connections and the influence of wars and their locations combined to affect the chronological and spatial variations in the numbers and types of travellers through the two centuries.

Fong與Vasicek（1997）提出風險分析應考慮敏感度分析、風險值及壓力測試，才能完整揭露投資組合的風險狀況。其中風險值的計算，不僅考慮二階風險，並且利用三階動差進行偏態修正。本文除了以變異數-共變異數法、歷史模擬法及蒙地卡羅模擬法此三種方法計算風險值，並利用Fong與Vasicek（1997）偏態修正法及Cornish-Fisher偏峰態修正法來做偏態及峰態的修正。而後再利用概似比檢驗法、回溯測試百分比法及Z檢定法作為驗證風險值模型的評比工具。我們建議在95%及99%的信賴水準下，求算風險值可利用Cornish-Fisher所提出的方法修正偏態及峰態。 / Fong and Vasicek (1997) mentioned that risk analysis should include sensitivity analysis, value at risk (VaR) and stress testing, in order to capture portfolio risk. The calculation of VaR should not only consider the second moment but should also adjust the skewness using the third moment. In this article, we determine VaR by employing three methods, the variance covariance, the historical simulation and the Monte Carlo simulation methods. In addition, we also adjust VaR for the skewness and kurtosis using the methods developed by Fong and Vasicek (1997) and Cornish-Fisher. Then, the likelihood ratio test, back testing and the Z-test are used to verify the VaR model. Our final test results suggest that calculating VaR should be adjusted for the skewness and the kurtosis as shown by the method proposed by Cornish Fisher in the 95% and 99% confidence intervals.

Employing Cornish Cultures for Community Resilience. Can cultural distinctiveness be used to strengthen community bonds, boost morale and equip and motivate people socially and economically? Using the witness of people in Cornwall and comparative experiences, this discussion combines a review of how cultures are commodified and portrayed with reflections on well-being and ‘emotional prosperity’. Cornwall is a relatively poor European region with a cultural identity that inspires an established ethno-cultural movement and is the symbolic basis of community awareness and aspiration, as well as the subject of contested identities and representations. At the heart of this is an array of cultures that is identified as Cornish, including a distinct post-industrial inheritance, the Cornish Language and Celtic Revivalism. Cultural difference has long been a resource for cultural industries and tourism and discussion of using culture for regeneration has accordingly concentrated almost exclusively on these sectors but an emergent ‘regional distinctiveness agenda’ is beginning to present Cornish cultures as an asset for use in branding and marketing other sectors. All of these uses ultimately involve commodification but culture potentially has a far wider role to play in fostering economic, social, cultural and environmental resilience. This research therefore uses multidisciplinary approaches to broaden the discussion to include culture’s primary emotional and social uses. It explores the possibility that enhancing these uses could help to tackle economic and social disadvantage and to build more cohesive communities. The discussion centres on four linked themes: multiple forms of capital; discourse, narrative and myth; human need, emotion and well-being; representation and intervention. Cultural, social, symbolic and human capital are related to collective status and well-being through consideration of cultural practices, repertoires and knowledge. These are explored with discussion of accompanying representations and discourses and their social, emotional and economic implications so as to allow tentative suggestions for intervention in policy and representation. A key conclusion is that culture may be used proactively to increase ‘emotional capital’.