arXiv subjects

Brajesh Kumar Dhakad

Publications and source records attributed to Brajesh Kumar Dhakad.

2 recordsLinked to original sources

arXiv2026

On Modeling Cylindrical Data with a Discrete Circular Component and Its Environmental Applications

Standard statistical methods are often inadequate for modeling the joint dependence between linear and circular variables, and existing methods for modeling this dependence are designed only for continuous variables. However, circular data are frequently observed on a finite set of equally spaced directions, either due to rounding prior to reporting or because of the experimental design employed for data collection. To address this gap, we propose a flexible, analytically tractable model for jointly representing a discrete circular and a continuous linear variable. The construction combines a wrapped symmetric geometric distribution, a Weibull distribution, and a trigonometric linking function. This formulation yields closed-form expressions for the joint, marginal, and conditional distributions. The choice of the Weibull distribution facilitates direct sample generation using the inverse transform technique. Additionally, it provides explicit expressions for conditional moments, enabling a flexible circular-linear regression framework. We detail the theoretical interpretation of the model parameters, mathematically establishing the monotonicity of the conditional mean and variance with respect to the dependence parameters. The performance of the estimators is demonstrated through extensive simulations, and the utility of the model is illustrated by analyzing two empirical environmental datasets.

stat.ME↗

arXiv2026

Some bivariate distributions on a discrete torus with application to wind direction datasets

Directional measurements such as wind directions are often recorded in a finite number of angular categories rather than as exact angles. When two such measurements are observed jointly, the resulting bivariate observations lie on a discrete torus. Commonly used bivariate circular models are formulated for continuous angular variables. Applying these models to categorical observations requires integrating their densities over regions corresponding to observed category pairs. We propose two parametric models defined directly on the discrete torus, with interpretable parameters for marginal locations and concentrations, and for dependence between the two circular variables. The models provide closed-form probability mass functions and trigonometric moments, which are used to show that, under certain conditions, the dependence parameter characterizes circular--circular correlation. Parameters are estimated by maximum likelihood, and the finite-sample performance is investigated through simulation. The proposed models are applied to three datasets of paired wind direction measurements recorded in 16 equally spaced compass directions at stations in India and compared with discretized versions of established continuous bivariate circular models. They provide competitive fits while allowing likelihood evaluation directly on the observed discrete support. The fitted models are also used to assess the dependence between the paired wind directions in each dataset.

stat.ME↗