A characteristic function based circular distribution family and its goodness of fit : The flexible wrapped Linnik family.

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 α 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.

Variable selection in linear-circular regression models.

Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity.

Multimodal exponential families of circular distributions with application to daily peak hours of PM2.5 level in a large city.

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.