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 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.