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：本文讨论了疾病潜伏期分布的非参数估计方法。传统方法通常采用威布尔分布、对数正态分布或伽马分布等参数族进行估计。我们转而分析非参数极大似然估计量（MLE），证明在特定条件下其收敛速度为立方根$n$，且极限行为服从切尔诺夫分布。基于该MLE，我们还研究了平滑估计方法。与经典参数方法相比，基于MLE的密度估计能够捕捉密度中更精细或非预期的特征。文中提供了非参数方法的R语言脚本。