In this paper, we introduced a new two-component nonparametric mixture model with a stochastic dominance constraint, a model arising naturally from many genetic studies. For this model, we proposed and studied two estimations. The first one is based on cumulative distribution functions with use of the stochastic dominance inequality, while the second one is a maximum likelihood estimation of the multinomial approximation of the model. For both methods, we not only proved their consistency but also examined their finite-sample performance through simulation studies. Our numerical studies showed that both methods work equivalently well. To demonstrate their implementation, we applied them to two real datasets.

在本文中，我们引入了具有随机优势约束的新的两成分非参数混合模型，该模型是许多遗传研究自然产生的。对于此模型，我们提出并研究了两种估计。第一个基于使用随机支配不等式的累积分布函数，第二个基于模型的多项式逼近的最大似然估计。对于这两种方法，我们不仅证明了它们的一致性，而且还通过仿真研究检查了它们的有限样本性能。我们的数值研究表明，两种方法都等效地工作。为了演示其实现，我们将它们应用于两个真实的数据集。