The extended power distribution: A new distribution on $(0, 1)$

We propose a two-parameter bounded probability distribution called the extended power distribution. This distribution on $(0, 1)$ is similar to the beta distribution, however there are some advantages which we explore. We define the moments and quantiles of this distribution and show that it is possible to give an $r$-parameter extension of this distribution ($r>2$). We also consider its complementary distribution and show that it has some flexibility advantages over the Kumaraswamy and beta distributions. This distribution can be used as an alternative to the Kumaraswamy distribution since it has a closed form for its cumulative function. However, it can be fitted to data where there are some samples that are exactly equal to 1, unlike the Kumaraswamy and beta distributions which cannot be fitted to such data or may require some censoring. Applications considered show the extended power distribution performs favourably against the Kumaraswamy distribution in most cases.