The extreme value theory (EVT) has been used to model and measure the distribution of extreme minima of Byco Petroleum in the Pakistan stock market over the period from 2005 to 2012. This paper covers the investigation of distributions that are mostly used in finance including the generalized extreme value (GEV), generalized logistics (GL), and generalized Pareto (GPA) distribution. L-moment ratio diagram is being used to find the appropriate distributions among the distributions. L-moment diagram depicts that GEV and GL distributions are suitable to represent the extremes of Byco Petroleum Pakistan Limited. Thereafter, the probability weighted moment (PWM) method has been used in order to estimate the parameters of probability distributions. Furthermore, Anderson–Darling (AD) goodness-of-fit test is employed to test the goodness of fit among GEV and GL distributions, and it is clear from the results that the GL distribution is more reliable and applicable for extreme minima of Byco Petroleum Company in the Pakistan stock exchange market. EVT and traditional methods are used for value-at-risk (VaR) analysis. The analysis indicates that EVT methods are more suitable for risk measurement in comparison with traditional methods.

中文翻译：

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基于极值理论的巴基斯坦Byco Petroleum风险分析与建模

极值理论 (EVT) 已被用于建模和测量 2005 年至 2012 年期间巴基斯坦股票市场 Byco Petroleum 的极小值分布。 本文涵盖了主要用于金融的分布调查，包括广义极值 (GEV)、广义物流 (GL) 和广义帕累托 (GPA) 分布。L 矩比率图用于在分布中找到合适的分布。L 矩图描绘了 GEV 和 GL 分布适合代表 Byco Petroleum Pakistan Limited 的极端情况。此后，使用概率加权矩（PWM）方法来估计概率分布的参数。此外，使用 Anderson-Darling (AD) 拟合优度检验来检验 GEV 和 GL 分布之间的拟合优度，从结果可以看出，GL 分布更可靠，更适用于 Byco Petroleum Company巴基斯坦证券交易所市场。EVT 和传统方法用于风险价值 (VaR) 分析。分析表明，与传统方法相比，EVT 方法更适合于风险度量。