标题： 从狄利克雷总体中抽样：估计物种数量 显示英文标题

标题： Sampling from Dirichlet populations: estimating the number of species

摘要： 考虑将区间随机划分为$n$个片段的狄利克雷划分，参数为$\theta >0$。 我们回顾了有限狄利克雷划分中的无序Ewens抽样公式。 由于这是估计的关键变量，重点在于抽样过程中访问的不同物种的数量。 这些在特定情况下进行了说明。 我们利用这些关于频率分布的初步统计结果来解决以下抽样问题：当从狄利克雷群体中抽样时，估计的物种数量是多少？ 所得结果与从具有泊松-狄利克雷分布的随机比例中进行抽样的理论结果一致。 最后，我们将所建议的各种估计器应用于两组不同的真实数据。 显示英文摘要

摘要： Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes, focus is on the number of distinct visited species in the sampling process. These are illustrated in specific cases. We use these preliminary statistical results on frequencies distribution to address the following sampling problem: what is the estimated number of species when sampling is from Dirichlet populations? The obtained results are in accordance with the ones found in sampling theory from random proportions with Poisson-Dirichlet distribution. To conclude with, we apply the different estimators suggested to two different sets of real data.