A brief determination of certain class of power semicircle distribution

In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gausshypergeometric function unlike the long proof in Roozegar and Soltani (2013).

Power semicircle distribution; Gauss-hypergeometric function; randomly weighted average; arcsine distribution.