I am seeking a parametric probability model whose pdf has the following characteristics: (1) it is supported on a variate axis that is bounded between 0 and 1; (2) it is continuous; and (3) it is capable of having two (or more) modes that are not necessarily located at 0 or 1 (e.g., in contrast to the beta distribution whose a and b are both <1). I am thinking of some sort expansion on the beta or Kumaraswamy distribution analogous to the bi-Weibull expansion on the Weibull distribution. My intention is to use such a model as a sampling distribution for sample proportions that vary continuously. My simulated data tend toward the low side of the variate range, typically ranging between 0 and 0.01, with a center of mass that in the neighborhood of 0.001. See the illustration below for examples. Has anyone run across such an obscure distribution that meets this challenging combination of criteria?