We introduce a discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent and identically distributed Bernoulli trials needed to observe either s successes or t failures. This report provides a closed-form expression for the mass function, moment generating function, and provides connections to other, standard distributions.

中文翻译：

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使用停止负二项分布的临床试验设计

我们引入了早期临床试验中常见的缩减抽样规则所建议的离散分布。我们推导出观察 s 次成功或 t 次失败所需的最小数量的独立同分布伯努利试验的分布。该报告为质量函数、力矩生成函数提供了封闭形式的表达式，并提供了与其他标准分布的连接。