A Meaningful Construction of New Circular Distribution for Applications in Geomorphology

Objectives: This work introduces a novel circular probability distributionthe Double Truncated Wrapped Exponential (DTWE) distribution highlighting the importance of circular statistics with cyclical characteristics contrary to usual linear data. Methods: The DTWE distribution is developed using the principle of truncation on the wrapped exponential distribution, which satisfies the principles of circularity. The properties of the distribution, such as the trigonometric mean, skewness, and kurtosis, are derived to enhance interpretability. Parameter estimation is carried out using Maximum Likelihood Estimation, Least Squares, and Weighted Least Squares methods. The goodness-of-fit is carried out, which makes DTWE distribution comparable to other well-known circular probability models. Findings: The numerical results of the simulation study across sample sizes (𝑛 = 30, 50, 100, 1000) and parameter values (𝜃 = 0.5, 1, 2) demonstrate that the DTWE distribution achieves accurate and consistent parameter estimation. For 𝜃 = 0.5 and 𝑛 = 30, the key performance metrics, such as the bias, Mean Square Error (MSE), and standard deviation (SD) for MLE outperform the LS and WLS methods by approximately 20%. Similarly, for 𝜃 = 2 and 𝑛 = 1000, the MLE achieves greater consistency reducing the bias, MSE, and SD by more than 30%. Real world data analysis shows that the DTWE distribution captures the cyclical patterns in ecological and geological data perfectly and gives meaningful insights into directional behaviours. Novelty: This study introduces a novel truncationbased framework for constructing circular probability distributions. The new distribution provides a distinctive approach for evaluating the circular data in ecological and geological datasets. Keywords: Directional Statistics; Truncation; Exponential Distribution; Circular Distribution; MLE