SenGupta Ashis, Roy Moumita
Department of Mathematics, Indian Institute of Technology, Kharagpur, India.
Department of Population Health Sciences, MCG Augusta University, Augusta, GA, USA.
J Appl Stat. 2023 Nov 21;51(12):2364-2381. doi: 10.1080/02664763.2023.2283689. eCollection 2024.
In this article, the primary aim is to introduce a new flexible family of circular distributions, namely the wrapped Linnik family which possesses the flexibility to model the inflection points and tail behavior often better than the existing popular flexible symmetric unimodal circular models. The second objective of this article is to obtain a simple and efficient estimator of the index parameter of symmetric Linnik distribution exploiting the fact that it is preserved in the wrapped Linnik family. This is an interesting problem for highly volatile financial data as has been studied by several authors. Our final aim is to analytically derive the asymptotic distribution of our estimator, not available for other estimator. This estimator is shown to outperform the existing estimator over the range of the parameter for all sample sizes. The proposed wrapped Linnik distribution is applied to some real-life data. A measure of goodness of fit proposed in one of the authors' previous works is used for the above family of distributions. The wrapped Linnik family was found to be preferable as it gave better fit to those data sets rather than the popular von-Mises distribution or the wrapped stable family of distributions.
在本文中，主要目的是引入一个新的灵活的圆形分布族，即包裹林尼克族，它具有比现有的流行灵活对称单峰圆形模型更好地对拐点和尾部行为进行建模的灵活性。本文的第二个目标是利用对称林尼克分布的指数参数在包裹林尼克族中得以保留这一事实，获得该指数参数的一个简单有效的估计量。正如几位作者所研究的，这对于高波动性金融数据来说是一个有趣的问题。我们的最终目标是解析地推导我们的估计量的渐近分布，这是其他估计量所不具备的。结果表明，对于所有样本量，在参数范围内该估计量都优于现有估计量。所提出的包裹林尼克分布被应用于一些实际数据。作者之前的一项工作中提出的拟合优度度量被用于上述分布族。结果发现包裹林尼克族更可取，因为它对那些数据集的拟合优于流行的冯·米塞斯分布或包裹稳定分布族。
