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.

中文翻译：

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球形狄利克雷分布

今天，数据挖掘和基因表达处于现代数据分析的最前沿。在这里，我们介绍了适用于这些领域的新型概率分布。本文开发了拟议的球面Dirichlet分布，旨在适合位于超球面正态上的矢量，因为这些字段中的数据经常出现这种情况，从而避免了不必要的概率质量。提出了建议分布的基本属性，包括归一化常数和矩。还探讨了与其他分布的关系。获得基于经典推论统计的估计器，例如矩量法和最大似然估计器。开发了两个应用程序：第一个使用模拟数据，第二个使用真实文本挖掘示例。