Investigating an Asymmetric Ratio Cosine Distribution

Abstract

Most real-world data have asymmetric features, slight or pronounced, that cannot be analyzed in depth using classical symmetric distributions. This is especially true when the underlying phenomena take their values in bounded support. Examples include data with support (−1, 1), which may correspond to daily temperature anomalies, stock market returns and satisfaction ratings, among others. Motivated by this last point, this article introduces a novel asymmetric cosine distribution of the ratio type. It aims to extend the functionalities of the classical cosine distribution by incorporating two adjustable parameters that allow for flexible levels of asymmetry. The main functions and theoretical properties such as moments, quantiles and distributional properties are studied. Some derived distributions are also established, extending the scope of the Cauchy and half-Cauchy distributions. Applications to simulated data in hypothetical environmental, financial and sentiment analysis scenarios demonstrate the practical utility of the asymmetric cosine distribution in capturing nuanced behavior.