The Wiener diffusion model with two absorbing barriers is frequently used in modeling decisions and decision latencies jointly. We derive representations of the partial derivatives of the density and cumulative distribution function of first-passage times. Different representations, based on infinite series, differ in convergence for small and large times, and we provide methods that control the approximation errors. These methods and their implementation in an R package are helpful whenever gradient information is required as is the case in many frequentist and Bayesian approaches to modeling.

中文翻译：

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维纳扩散模型中首过时间分布的偏导数

具有两个吸收障碍的 Wiener 扩散模型经常用于联合建模决策和决策延迟。我们推导出密度和首次通过时间的累积分布函数的偏导数的表示。基于无穷级数的不同表示在小时间和大时间的收敛性不同，我们提供了控制近似误差的方法。这些方法及其在R包中的实现在需要梯度信息时很有帮助，就像许多频率论和贝叶斯建模方法一样。