A new generalization of the extreme value distribution is presented with its density function, having a wide variety of density and tail shapes for modeling extreme value data. This generalized extreme value distribution will be referred to as the odd generalized extreme value distribution. It is derived by considering the distributions of the odds of the generalized extreme value distribution. Consequently, the new distribution is enlightened by not only having all six families of extreme value distributions; Gumbel, Fréchet, Weibull, reverse-Gumbel, reverse-Fréchet, and reverse-Weibull as submodels but also convenient for modeling bimodal extreme value data that are frequently found in environmental sciences. Basic properties of the distribution, including tail behavior and tail heaviness, are studied. Also, quantile-based aliases of the new distribution are illustrated using Galton's skewness and Moor's kurtosis plane. The adequacy of the new distribution is illustrated using well-known goodness-of-fit measures. A simulation is performed to validate the estimated risk measures due to repeated data points frequently found in temperature data. The Grand Rapids and well-known Wooster temperature data sets are analyzed and compared to nine different extreme value distributions to illustrate the new distribution's bimodality, flexibility, and overall fitness.

中文翻译：

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新的广义极值分布及其在极端温度数据中的应用

极值分布的新推广及其密度函数提出了，具有多种密度和尾部形状用于对极值数据进行建模。该广义极值分布将被称为奇广义极值分布。它是通过考虑广义极值分布的赔率分布而得出的。因此，新的分布不仅具有所有六个极值分布族，而且具有极值分布的特征。 Gumbel、Fréchet、Weibull、反向 Gumbel、反向 Fréchet 和反向 Weibull 作为子模型，也方便对环境科学中常见的双峰极值数据进行建模。研究了分布的基本属性，包括尾部行为和尾部重量。此外，新分布的基于分位数的别名使用高尔顿偏度和摩尔峰度平面进行说明。使用众所周知的拟合优度度量来说明新分布的充分性。进行模拟是为了验证由于温度数据中经常出现的重复数据点而估计的风险措施。对大急流城和著名的伍斯特温度数据集进行了分析，并与九种不同的极值分布进行比较，以说明新分布的双峰性、灵活性和整体适应性。