Abstract

In this note, we develop a novel algorithm for generating random numbers from a distribution with a probability density function proportional to ${\hspace{0.17em}\text{sin}\hspace{0.17em}}^k(x),x\in (0,\pi )$ and $k\ge 1.$ Our algorithm is highly efficient and is based on rejection sampling where the envelope distribution is an appropriately chosen beta distribution. An example application illustrating how the new algorithm can be used to generate random correlation matrices is discussed.

中文翻译：

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一种从 sink (x) 采样以生成随机相关矩阵的有效算法

摘要

在这篇笔记中，我们开发了一种新的算法，用于从具有与成比例的概率密度函数的分布生成随机数${\hspace{0.17em}\text{罪}\hspace{0.17em}}^{ķ}(X),X\in (0,\pi )$和$ķ\ge 1.$Our algorithm is highly efficient and is based on rejection sampling where the envelope distribution is an appropriately chosen beta distribution. 讨论了说明如何使用新算法生成随机相关矩阵的示例应用程序。