The wrapping Epanechnikov exponential distribution: A novel flexible model for asymmetric circular data

Abstract

This study introduces the Wrapped Epanechnikov Exponential Distribution (WEED), a novel circular distribution derived from the Epanechnikov exponential distribution. The probability density function and cumulative distribution function are presented, together with a comprehensive analysis of its properties and parameters, including the characteristic function and trigonometric moments. Parameters are estimated using maximum likelihood estimation (MLE). A simulation study with 10,000 samples demonstrates the consistency of the MLE method, with bias decreasing from 0.14221 to 0.03203 and MSE improving from 0.03456 to 0.00163 for β=1 as sample size increases from N = 30 to N = 500. Applications to real-world datasets confirm WEED’s superior flexibility compared to established models, achieving lower AIC values across multiple datasets (Wind direction: 100.72 vs. 112.907; Turtle orientation: 142.764 vs. 145.254; Fisher-B5: 77.6998 vs. 79.833) when compared with the Wrapped Exponential Distribution (WED). Kolmogorov–Smirnov tests further support WEED’s improved goodness-of-fit, with consistently lower test statistics across all datasets. This work contributes to the field of circular statistics by providing a promising tool for modeling asymmetric circular data with enhanced flexibility and accuracy.