标题： 引入广义伽马分布：一种用于指数标准化的灵活分布 显示英文标题

标题： Introducing the generalized gamma distribution: a flexible distribution for index standardization

摘要： 渔业科学家使用回归模型来估计种群数量，如生物量或丰度，用于气候、栖息地、种群和生态系统评估。 然而，这些模型对用于描述观测误差的概率分布的选择很敏感。 在这里，我们介绍了广义伽马分布（GGD），它在渔业科学中尚未被广泛使用。 GGD具有有用的特点：（1）当形状参数接近零时，它会退化为对数正态分布；（2）当形状参数和尺度参数相等时，它会退化为伽马分布；以及（3）变异系数与均值无关。 我们在一个模拟实验中评估了GGD在不同类型的观测误差下估计生物量密度的相对性能和稳健性。 当拟合由GGD、对数正态分布、伽马分布和Tweedie族生成的数据时，GGD表现出低偏差和高预测准确性。 最后，我们使用R包sdmTMB拟合了时空指数标准化模型，数据来自加拿大阿拉斯加湾和不列颠哥伦比亚省海岸的三个拖网调查中的15个物种。 当比较使用对数正态分布、伽马分布和Tweedie族拟合的模型之间的Akaike信息准则（AIC）权重时，GGD是最常被选择的模型。 显示英文摘要

摘要： Fisheries scientists use regression models to estimate population quantities, such as biomass or abundance, for use in climate, habitat, stock, and ecosystem assessments. However, these models are sensitive to the chosen probability distribution used to characterize observation error. Here, we introduce the generalized gamma distribution (GGD), which has not been widely used in fisheries science. The GGD has useful properties: (1) it reduces to the lognormal distribution when the shape parameter approaches zero; (2) it reduces to the gamma distribution when the shape and scale parameters are equal; and (3) the coefficient of variation is independent of the mean. We assess the relative performance and robustness of the GGD to estimate biomass density across different observation error types in a simulation experiment. When fit to data generated from the GGD, lognormal, gamma, and Tweedie families, the GGD had low bias and high predictive accuracy. Finally, we fit spatiotemporal index standardization models using the R package sdmTMB to 15 species from three trawl surveys from the Gulf of Alaska and coast of British Columbia, Canada. When the Akaike information criterion (AIC) weight was compared among fits using the lognormal, gamma, and Tweedie families the GGD was the most commonly selected model.