Development and analysis of a new trigonometric unit distribution

Abstract

In this paper, we introduce a novel trigonometric unit distribution that generalizes the uniform distribution through a single shape parameter. We derive its main properties, including closed-form expressions for the cumulative distribution function and the mean. We then study the associated statistical model and assess its inferential performance using maximum likelihood estimation. A simulation study confirms the effectiveness of the proposed estimation procedure. Applications to two real data sets show that the new model provides greater flexibility and achieves competitive goodness-of-fit compared with traditional alternatives.