标题： 关于球面Dirichlet分布：修正与结果 显示英文标题

标题： On the Spherical Dirichlet Distribution: Corrections and Results

摘要： 本文纠正了Guardiola（2020，统计分布与应用期刊）中的一个技术错误，呈现了更新的推导，并对球面Dirichlet分布的性质进行了扩展讨论。如今，数据挖掘和基因表达处于现代数据分析的前沿。在此，我们介绍了一种适用于这些领域的新型概率分布。本文发展了提议的球面-Dirichlet分布，旨在适合位于超球正象限的向量，因为这种情况在这些领域的数据中经常出现，从而避免不必要的概率质量。提出了所提议分布的基本性质，包括归一化常数和矩。还探讨了与其他分布的关系。基于经典推断统计方法（如矩法估计和最大似然估计）得到了估计器。开发了两个应用：第一个使用模拟数据，第二个使用真实的文本挖掘实例。这两个例子均使用提议的球面-Dirichlet分布进行拟合，并讨论了其结果。 显示英文摘要

摘要： This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution. Today, data mining and gene expressions are at the forefront of modern data analysis. Here we introduce a novel probability distribution that is applicable in these fields. This paper develops the proposed Spherical-Dirichlet Distribution designed to fit vectors located at the positive orthant of the hypersphere, as it is often the case for data in these fields, avoiding unnecessary probability mass. Basic properties of the proposed distribution, including normalizing constants and moments are developed. Relationships with other distributions are also explored. Estimators based on classical inferential statistics, such as method of moments and maximum likelihood estimators are obtained. Two applications are developed: the first one uses simulated data, and the second uses a real text mining example. Both examples are fitted using the proposed Spherical-Dirichlet Distribution and their results are discussed.