The log-cosine-power unit distribution : a new unit distribution for proportion data analysis

Continuous formulations of new distributions defined on the unit interval have gained attention because of their relevance in modeling proportion data. We innovate in this research direction by combining logarithmic, cosine, and power functions to create a log-cosine-power cumulative distribution function that defines the log-cosine-power distribution. The corresponding probability density has the originality of having the tangent function as the primary term. Furthermore, graphical analysis shows that the log-cosine-power distribution can produce a truly attractive model: the probability density function is capable of in-depth analysis of proportion data exhibiting inverted-J, J, and decreasing-constant-increasing shapes. This modeling power is demonstrated using two datasets, and results reveal that it has the potential to provide a better parametric fit to proportional data than other existing distributions with support defined on the unit interval.