Neutrosophic von Mises Distribution for Indeterminate Circular Data

In this paper, we consider the neutrosophic von Mises distribution for circular data with indeterminacy. The proposed distribution extends the classical von Mises model within a neutrosophic framework, allowing the indeterminacy represented by observed angular arcs to be retained in the analysis. Its main statistical properties are derived, including the trigonometric moments, mean direction, mean resultant length, circular variance, circular standard deviation, modal direction, and entropy. Maximum likelihood estimators of the model parameters are obtained, and their finite-sample performance is examined through a Monte Carlo simulation study. The practical use of the proposed distribution is illustrated with real circular data, where model adequacy is assessed through goodness-of-fit analysis and graphical comparison with nonparametric circular kernel density estimates.