Replication of linear functional relationship model for circular variables

The study involves circular data models and multiple outlier detection method. A linear functional relationship model (LFRM) with maximum likelihood parameters and covariance matrices is considered because previous studies had constraints and conditions for some parameters. This study introduces General Unreplicated LFRM (GULFRM) and General Replicated LFRM (GRLFRM). The maximum likelihood method evaluates all estimated parameters in all these models because circular data is expected to follow the von Mises distribution. Monte Carlo simulations validate the models. The simulation results show that the proposed parameter estimates produce a modest mean bias and a small squared mean error estimator, proving their effectiveness. A clustering-based pseudo-replicates model transforms unreplicated into replicated circular data. GRLFRM can analyse unreplicated data after replication. Monte Carlo simulations verify this pseudo-replicate model. The simulations show that the proposed parameter estimations have low bias, validating the model's efficacy. A method for identifying multiple outliers in circular data comes next. COVRATIO uses the covariance matrix determinant equation generated from GULFRM and GRLFRM to detect outlier points. The cut-off point equations use the simulation study's 5% upper percentile with 95% confidence level. Monte Carlo simulation experiments with outlier points are performed to assess method efficiency. According to simulations, as contamination level increases, the outlier points detection procedure approaches 100% detection. The study shows that COVRATIO is a valid strategy for detecting multiple outliers. A complete general cycle of circular data analysis is the study's key novelty. Circular data analysis has four paths. Circular data can be analysed in any form under any circumstance with this four-path cycle of circular analysis.