A Wrapped New Polynomial One-Parameter Distribution with Applications to Ecological and Wind Direction Data

Abstract

Observations recorded as angles or directions appear across a wide range of scientific fields, from ecology and en- vironmental to atmospheric science and materials research. Because such circular data follow a periodic structure, standard statistical tools fail to capture their geometry, and purpose-built circular distributions are required. This study proposes the Wrapped New Polynomial Single-Parameter (WNPS) distribution, a novel one-parameter circular model constructed by wrapping the New Polynomial Single-Parameter distribution onto the unit circle. A systematic study of its mathematical structure gives the closed-form expressions for the survival function, hazard rate, modality condi- tions, characteristic function, trigonometric moments,invariance behavior and Renyi entropy measures. Also, various ´ characterizations of the proposed distribution are presented. Parameter estimation is addressed through ten frequen- tist procedures alongside a Bayesian framework employing five loss functions from both symmetric and asymmetric penalization. Monte Carlo simulation experiment compares the finite-sample behavior of all estimators across vary- ing sample sizes and parameter configurations. The usefulness of the WNPS distribution in practice is illustrated via two real-life datasets consisting of angular measurements from an ecological study and another on wind direction. Goodness-of-fit comparisons against the wrapped Lindley, wrapped modified Lindley, wrapped XLindley, and related competitors confirm the WNPS distribution as a competitive and parsimonious choice for circular data modeling.