arXiv subjects

Jayant Jha

Publications and source records attributed to Jayant Jha.

6 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.

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arXiv2026

Modeling Zero-Inflated Longitudinal Circular Data Using Bayesian Methods: Application to Ophthalmology

This paper introduces the modeling of circular data with excess zeros under a longitudinal framework, where the response is a circular variable and the covariates can be both linear and circular in nature. In the literature, various circular-circular and circular-linear regression models have been studied and applied to different real-world problems. However, there are no models for addressing zero-inflated circular observations in the context of longitudinal studies. Motivated by a real case study, a mixed-effects two-stage model based on the projected normal distribution is proposed to handle such issues. The interpretation of the model parameters is discussed and identifiability conditions are derived. A Bayesian methodology based on Gibbs sampling technique is developed for estimating the associated model parameters. Simulation results show that the proposed method outperforms its competitors in various situations. A real dataset on post-operative astigmatism is analyzed to demonstrate the practical implementation of the proposed methodology. The use of the proposed method facilitates effective decision-making for treatment choices and in the follow-up phases.

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arXiv2025

Adjusting SPRT for an Efficient Procedure with Finite Number of Applications of Less Effective Treatment

We propose an adaptive Sequential Probability Ratio Test (SPRT) which allocates a finite number of applications to the less effective treatment. In the classical SPRT framework, patients are assigned to the two competing treatments one by one until the stopping criterion, based on breaching the boundary values which are pre-determined using the Type-I and Type-II error probabilities, is met. This ensures the control of errors at the cost of ethical efficiency as the exposure to the less effective treatment is large. We begin with proposing an adaptive sequential framework for testing two simple hypotheses that analytically ensures finite exposure to the less effective treatment. Our proposed procedure employs a likelihood ratio driven adaptive allocation rule, dynamically concentrating sampling effort on the superior population while preserving asymptotic efficiency (in terms of average sample number), comparable to the classical SPRT. We derive an explicit closed-form expression for the expected number of allocations to the inferior treatment. Extensive simulation studies and real data analyses substantiate the theoretical results, evincing a significant reduction in inferior allocations compared to the classical SPRT. The proposed design thus offers a balanced method between statistical precision and ethical responsibility, aligning inferential reliability with patient safety.

math.ST↗

arXiv2025

To Study Properties of a Known Procedure in Adaptive Sequential Sampling Design

We consider the procedure proposed by Bhandari et al. (2009) in the context of two-treatment clinical trials, with the objective of minimizing the applications of the less effective drug to the least number of patients. Our focus is on an adaptive sequential procedure that is both simple and intuitive. Through a refined theoretical analysis, we establish that the number of applications of the less effective drug is a finite random variable whose all moments are also finite. In contrast, Bhandari et al. (2009) observed that this number increases logarithmically with the total sample size. We attribute this discrepancy to differences in their choice of the initial sample size and the method of analysis employed. We further extend the allocation rule to multi-treatment setup and derive analogous finiteness results, reinforcing the generalizability of our findings. Extensive simulation studies and real-data analyses support theoretical developments, showing stabilization in allocation and reduced patient exposure to inferior treatments as the total sample size grows. These results enhance the long-term ethical strength of the proposed adaptive allocation strategy.

math.ST↗

arXiv2020

Two-stage Circular-circular Regression with Zero-inflation: Application to Medical Sciences

This paper considers the modeling of zero-inflated circular measurements concerning real case studies from medical sciences. Circular-circular regression models have been discussed in the statistical literature and illustrated with various real-life applications. However, there are no models to deal with zero-inflated response as well as a covariate simultaneously. The Mobius transformation based two-stage circular-circular regression model is proposed, and the Bayesian estimation of the model parameters is suggested using the MCMC algorithm. Simulation results show the superiority of the performance of the proposed method over the existing competitors. The method is applied to analyse real datasets on astigmatism due to cataract surgery and abnormal gait related to orthopaedic impairment. The methodology proposed can assist in efficient decision making during treatment or post-operative care.

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