Radiation therapy is a well established modality for treating various cancers. Planning for radiotherapy typically involves solving an inverse problem to find a clinically suitable plan. Optimization models and methods are used to address this task. During the planing, one of the most clinically relevant treatment planning objectives is to find a treatment plan that satisfies the so-called partial volume constraints on the resulting dose distribution. A conventional mixed-integer formulation of these partial volume constraints leads to a computationally intractable model which in practice becomes extremely difficult to solve. We analyze the effects of multiple gEUD-type constraints on the resulting dose-volume distribution – a convex and tractable alternative to partial volume constraints. The analysis relies on interpreting the dose distribution as a cumulative probability distribution of the underlying random variable that represents the dose to the treatment volume. Consequently, the above problem is rephrased in terms of a well studied problem of moments. We illustrate our approach on one organ at risk for prostate cancer.