A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design. One application is destructive duration analysis, where the process is censored at an observation test time. Another is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values placed by consumers on a public good such as endangered species. Sample consumers are asked whether they would vote for a referendum that would provide the good at a cost speciﾅed by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem.