A Proposal of New Extended Symmetric Cosine Distribution

Abstract

This article presents an extended symmetric version of the cosine distribution. The corresponding probability density function is constructed by a special linear combination of cosine and sine functions. These trigonometric functions are activated by two adjustable parameters with the aim of generating modulable oscillatory shapes. This gives the new distribution greater flexibility and applicability than the cosine distribution. Its main characteristics are then examined, focusing on its functional properties, the key moment measures and the generation of distributions with different support. A new skewed version of the standard normal distribution is also derived. Potential applications in various fields are discussed. Two simulated data examples are presented and analyzed, showing the superior performance of the new distribution compared to another two-parameter extended version of the cosine distribution.