An efficient algorithm for sampling from $\sin^k(x)$ for generating random correlation matrices

In this note, we develop a novel algorithm for generating random numbers from a distribution with a probability density function proportional to $\sin^k(x)$, $x \in (0,\pi)$ and $k \geq 1$. Our algorithm is highly efficient and is based on rejection sampling where the envelope distribution is an appropriately chosen beta distribution. An example application illustrating how the new algorithm can be used to generate random correlation matrices is discussed.