“…By letting X 1 and X 2 to have identical distributions, he derived that: (i) for X 1 and X 2 on [−1, 1], Z is uniform on [−1, 1] if and only if X 1 and X 2 have arcsin distribution; and (ii) Z possesses the same distribution as X 1 and X 2 if and only if X 1 and X 2 are degenerated or have a Cauchy distribution. Soltani and Homei (2009a) extended Van Assche's results as follows: They put X 1 , · · · , X n to be independent, and considered for n ≥ 2 S n (R 1 , ..., R n−1 ) = R 1 X 1 + R 2 X 2 + · · · + R n−1 X n−1 + R n X n , (1.1) 1], and U (0) = 0. Soltani and Roozegar (2012), defined fairly large classes of randomly weighted average (RWA) distributions by using new random weights.…”