A new family of distributions for circular data

Abstract A new method for constructing distributions for circular data is proposed. The method is based on piecewise probability density functions, in which two beta-type components are joined at a data-driven cut-point subject to continuity and periodicity conditions. The resulting family of distributions admits closed-form expressions for the cumulative distribution function, trigonometric moments, mean angle, mean resultant length, circular variance, Rényi entropy and Shannon entropy, and is simpler to compute than existing models since it relies only on the incomplete beta function, a widely supported special function. Maximum likelihood estimation is developed in detail, and the finite-sample behaviour of the estimators is examined through an extensive simulation study covering five representative parameter configurations. The proposed distribution is fitted to five real circular data sets and compared with seven competing models, including the distributions due to Jones and Pewsey 14 and Kato and Jones 15 . In every case, the proposed distribution attains the smallest AIC and BIC values and the largest Kuiper test p -value, providing consistent evidence of superior fit over all competitors.