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.

翻译：渔业科学家使用回归模型来估算种群数量，如生物量或丰度，以用于气候、栖息地、种群和生态系统评估。然而，这些模型对用于表征观测误差的概率分布的选择非常敏感。本文引入广义Gamma分布（GGD），该分布在渔业科学中尚未得到广泛应用。GGD具有以下有用特性：（1）当形状参数趋近于零时，它退化为对数正态分布；（2）当形状参数与尺度参数相等时，它退化为Gamma分布；（3）变异系数与均值无关。我们通过模拟实验评估了GGD在不同观测误差类型下估算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、Gamma分布和Tweedie族生成的数据时，GGD表现出低偏差和高预测精度。最后，我们使用R包sdmTMB对来自阿拉斯加湾和加拿大不列颠哥伦比亚省海岸的三项拖网调查中的15个物种拟合了时空指数标准化模型。通过比较使用对数正态分布、Gamma分布和Tweedie族拟合的赤池信息量准则（AIC）权重，GGD是最常被选中的模型。