Primary nucleation is a stochastic process; hence, detection times are statistically distributed even though experiments are repeated at the same conditions. This contribution aims at defining and discussing a method to perform an accurate statistical analysis of detection times; it focuses on three main aspects. First, we develop an accurate experimental protocol and set criteria on temperature, T, and supersaturation, S, to accept measurements as part of the experimental series. Applying such protocol to the isonicotinamide–ethanol system at several different supersaturations, we perform multiple series of isothermal nucleation experiments, calculating for each series the associated empirical cumulative distribution function (eCDF) of the detection times. Second, exploiting a set of statistical tools, we investigate whether the repetitions of the experiments at the same supersaturation conditions belong to the same stochastic process, assessing also the possibility to combine them in one single distribution. Third, we estimate for the eCDFs the values of its associated nucleation rate and derive an analytical expression to calculate the propagation of the uncertainty from the eCDF to the nucleation rate estimate.

中文翻译：

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用于估计成核速率的一系列检测时间测量值的统计分析

初级成核是一个随机过程。因此，即使在相同条件下重复进行实验，检测时间也会统计分布。该贡献旨在定义和讨论一种对检测时间进行准确统计分析的方法。它着重于三个主要方面。首先，我们开发出准确的实验方案并设定温度T和过饱和S的标准，以接受测量值作为实验系列的一部分。将这样的方案应用到处于不同过饱和状态的异烟酰胺-乙醇系统，我们执行了多个等温成核实验，为每个系列计算了检测时间的相关经验累积分布函数（eCDF）。其次，利用一套统计工具，我们研究在相同的过饱和条件下重复进行的实验是否属于同一随机过程，还评估了将它们组合成一个单一分布的可能性。第三，我们为eCDF估计其相关成核速率的值，并导出解析表达式以计算从eCDF到成核速率估计的不确定性传播。