On a new distribution based on the arccosine function

Abstract This note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this has exact function as density function. To our knowledge, despite obvious mathematical interest, such never been considered in Probability Statistics. Here, we fill gap by pointing out main properties proposed distribution, from both theoretical practical aspects. Specifically, provide analytical form expressions for its cumulative function, survival hazard rate raw moments incomplete moments. The asymptotes shape functions are described, well skewness kurtosis properties, revealing flexible nature distribution. In particular, it appears to be “round mesokurtic” “left skewed”. With these features mind, attention is given find empirical applications real data sets. Accordingly, compared with well-known means two