A Half-Circular Distribution on a Circle

Half circular modified burr−III distribution, application with different estimation methods

The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr−III distribution, called the half circular modified Burr−III (hcMB−III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB−III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. Finally, one data set related to posterior corneal curvature of the eyes of 23 patients, is analyzed to check potentiality of the newly proposed model.

Sequentially estimating the dynamic contact angle of sessile saliva droplets in view of SARS-CoV-2

Estimating the contact angle of a virus infected saliva droplet is seen to be an important area of research as it presents an idea about the drying time of the respective droplet and in turn of the growth of the underlying pandemic. In this paper we extend the data presented by Balusamy, Banerjee and Sahu ["Lifetime of sessile saliva droplets in the context of SARS-CoV-2," Int. J. Heat Mass Transf. 123, 105178 (2021)], where the contact angles are fitted using a newly proposed half-circular wrapped-exponential model, and a sequential confidence interval estimation approach is established which largely reduces both time and cost with regards to data collection.