In this paper we integrate isotonic regression with Stone's cross-validation-based method to estimate a distribution with a general countable support with a partial order relation defined on it. We prove that the estimator is strongly consistent for any underlying distribution, derive its rate of convergence, and in the case of one-dimensional support we obtain Marshal-type inequality for cumulative distribution function of the estimator. Also, we construct the asymptotically correct conservative global confidence band for the estimator. It is shown that, first, the estimator performs good even for small sized data sets, second, the estimator outperforms in the case of non-isotonic underlying distribution, and, third, it performs almost as good as Grenander estimator when the true distribution is isotonic. Therefore, the new estimator provides a trade-off between goodness-of-fit, monotonicity and quality of probabilistic forecast. We apply the estimator to the time-to-onset data of visceral leishmaniasis in Brazil collected from $2007$ to $2014$.

翻译：本文结合等渗回归与斯通基于交叉验证的方法，估计具有一般可数支撑集且其上定义偏序关系的分布。我们证明该估计量对任意潜在分布具有强相合性，推导其收敛速率，并在一维支撑集情形下获得估计量累积分布函数的马歇尔型不等式。同时，我们构建了该估计量的渐近正确保守全局置信带。研究表明：首先，该估计量即使在小型数据集上表现良好；其次，在非等渗潜在分布情形下优于基准方法；第三，当真实分布为等渗时，其表现几乎与格伦南德估计量相当。因此，新估计量在拟合优度、单调性与概率预测质量之间提供了权衡。我们将该估计量应用于巴西2007年至2014年收集的内脏利什曼病发病时间数据。