Uniform designs are widely used for experiments with mixtures. The uniformity of the design points is usually evaluated with a discrepancy criterion. In this paper, we propose a new criterion to measure the deviation between the design point distribution and a Dirichlet distribution. The support of the Dirichlet distribution, is defined by the set of d-dimensional vectors whose entries are real numbers in the interval [0,1] such that the sum of the coordinates is equal to 1. This support is suitable for mixture experiments. Depending on its parameters, the Dirichlet distribution allows symmetric or asymmetric, uniform or more concentrated point distribution. The difference between the empirical and the target distributions is evaluated with the Kullback–Leibler divergence. We use two methods to estimate the divergence: the plug-in estimate and the nearest-neighbor estimate. The resulting two criteria are used to build space-filling designs for mixture experiments. In the particular case of the flat Dirichlet distribution, both criteria lead to uniform designs. They are compared to existing uniformity criteria. The advantage of the new criteria is that they allow other distributions than uniformity and they are fast to compute.

均匀设计广泛用于混合物实验。设计点的均匀性通常用差异标准来评估。在本文中，我们提出了一种新的标准来衡量设计点分布与狄利克雷分布之间的偏差。狄利克雷分布的支持由一组 d 维向量定义，其条目是区间 [0,1] 中的实数，使得坐标之和等于 1。此支持适用于混合实验。根据其参数，狄利克雷分布允许对称或不对称、均匀或更集中的点分布。经验分布与目标分布之间的差异通过 Kullback-Leibler 散度进行评估。我们使用两种方法来估计散度：插件估计和最近邻估计。由此产生的两个标准用于构建混合实验的空间填充设计。在平坦狄利克雷分布的特殊情况下，这两个标准都会导致均匀设计。将它们与现有的均匀性标准进行比较。新标准的优点是它们允许除均匀性之外的其他分布，并且计算速度很快。