Estimation of the generalized Laplace distribution and its projection onto the circle

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-06-01 DOI:10.1016/j.spl.2025.110460

Marco Geraci

引用次数: 0

Abstract

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 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. A real data example is given in Supplementary Materials.

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广义拉普拉斯分布的估计及其在圆上的投影

广义拉普拉斯（GL）分布属于广义双曲分布的大族，由于其形状参数，它提供了一个处理各种应用的通用模型。椭圆对称的GL允许极坐标表示，可以用来产生圆形分布，我们称之为投影GL分布。后者在实际应用中似乎尚未得到考虑。在本文中，我们探索了一种易于实现的基于高斯正交的最大似然估计策略，用于GL的尺度混合表示及其在圆上的投影。通过仿真研究，将拟合程序与备选估计方法进行比较，以评估其可行性，同时将投影GL模型与其他流行的圆形分布进行对比。在补充资料中给出了一个真实的数据示例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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