Kim Sungsu, SenGupta Ashis
Department of mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA.
Applied statistics unit, Indian Statistical Institute, Kolkata, India.
J Appl Stat. 2020 Jul 23;48(16):3193-3207. doi: 10.1080/02664763.2020.1796938. eCollection 2021.
In this paper, we propose two multimodal circular distributions which are suitable for modeling circular data sets with two or more modes. Both distributions belong to the regular exponential family of distributions and are considered as extensions of the von Mises distribution. Hence, they possess the highly desirable properties, such as the existence of non-trivial sufficient statistics and optimal inferences for their parameters. Fine particulates (PM2.5) are generally emitted from activities such as industrial and residential combustion and from vehicle exhaust. We illustrate the utility of our proposed models using a real data set consisting of fine particulates (PM2.5) pollutant levels in Houston region during Fall season in 2019. Our results provide a strong evidence that its diurnal pattern exhibits four modes; two peaks during morning and evening rush hours and two peaks in between.
在本文中，我们提出了两种多峰圆形分布，它们适用于对具有两个或更多模式的圆形数据集进行建模。这两种分布都属于正则指数分布族，并被视为冯·米塞斯分布的扩展。因此，它们具有非常理想的性质，例如存在非平凡的充分统计量以及对其参数的最优推断。细颗粒物（PM2.5）通常来自工业和居民燃烧等活动以及车辆尾气排放。我们使用一个由2019年秋季休斯顿地区细颗粒物（PM2.5）污染物水平组成的真实数据集来说明我们提出的模型的效用。我们的结果提供了强有力的证据，表明其日变化模式呈现出四种模式；在早晚高峰时段各有两个峰值，中间还有两个峰值。
