We discuss nonparametric estimators of the distribution of the incubation time of a disease. The classical approach in these models is to use parametric families like Weibull, log-normal or gamma in the estimation procedure. We analyze instead the nonparametric maximum likelihood estimator (MLE) and show that, under some conditions, its rate of convergence is cube root $n$ and that its limit behavior is given by Chernoff's distribution. We also study smooth estimates, based on the MLE. The density estimates, based on the MLE, are capable of catching finer or unexpected aspects of the density, in contrast with the classical parametric methods. {\tt R} scripts are provided for the nonparametric methods.

翻译：我们讨论疾病孵化时间分布的非参数估计值。 这些模型的经典方法是在估计程序中使用Weibull、log-正常或伽马等参数家庭。 我们分析的是非参数最大可能性估计值(MLE), 并表明,在某些条件下,其趋同率是立方根$, 其极限行为由Chernoff的分布给出。 我们还根据MLE研究平稳估计值。 基于MLE的密度估计值, 与典型的参数估计方法不同, 其密度能够捕捉到更细或出乎意料的密度方面。 为非参数方法提供了脚本。 \ tR} 为非参数方法提供了脚本 。