The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically symmetric GL admits a polar representation that can be used to yield a circular distribution, which we call \emph{projected} GL distribution. The latter does not appear to have been considered yet in practical applications. In this article, we explore an easy-to-implement maximum likelihood estimation strategy based on Gaussian quadrature for the scale-mixture representation of the GL and its projection onto the circle. A simulation study is carried out to benchmark the fitting routine against alternative estimation methods to assess its feasibility, while the projected GL model is contrasted with other popular circular distributions.

翻译：广义拉普拉斯（GL）分布属于广义双曲分布族，因其形状参数而成为处理多种应用场景的灵活模型。椭圆对称的GL分布具有极坐标表示，可用于推导出一种圆周分布，我们称之为\emph{投影}GL分布。后者在实际应用中似乎尚未被考虑。本文针对GL分布及其圆周投影的尺度混合表示，探索了一种基于高斯求积的易于实现的最大似然估计策略。通过模拟研究，将该拟合程序与替代估计方法进行基准比较以评估其可行性，同时将投影GL模型与其他常用圆周分布进行对比。