Browsing by Subject "Q-Q plot"

In the fields of insurance and financial mathematics, robust modeling tools are essential for accura tely assessing extreme events. While standard statistical tools are effective for data with light-tailed distributions, they face significant challenges when applied to data with heavy-tailed characteristics. Identifying whether data follow a light- or heavy-tailed distribution is particularly challenging, often necessitating initial visualization techniques to provide insights into the nature of the distribution and guide further statistical analysis. This thesis focuses on visualization techniques, employing basic visual techniques to examine the tail behaviors of probability distributions, which are crucial for understanding the implications of extreme values in financial and insurance risk assessments. The study systematically applies a series of visualizations, including histograms, Q-Q plots, P-P plots, and Hill plots. Through the interpretation of these techniques on known distributions, the thesis aims to establish a simple framework for analyzing unknown data. Using Danish fire insurance data as our empirical data, this research simulates various probability distributions, emphasizing the visual distinction between light-tailed and heavy-tailed distributions. The thesis examines a range of distributions, including Normal, Exponential, Weibull, and Power Law, each selected for its relevance in modeling different aspects of tail behavior. The mathema tical exploration of these distributions provides a standard basis for assessing their effectiveness in capturing the nature of possibility of extreme events in data. The visual analysis of empirical data reveals the presence of heavy-tailed characteristics in the Danish fire insurance data and is not very well modeled by common light-tailed models such as the Normal and Exponential distributions. These findings underscore the need for more refined approaches that better accommodate the complexities of heavy-tailed phenomena. The thesis advocates for the further use of more advanced statistical tools and extreme value theory to asses heavy-tailed behaviour more accurately. Such tools are important for developing financial and insurance models that can effectively handle the extremities present in real-world data. This thesis contributes to the understanding and application of visualization techniques in the analysis of heavy-tailed data, laying a foundation to build on with more advanced tools to have more accurate risk management practices in the financial and insurance sectors.