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. Applications include bioassay and destructive duration analysis. The empirical application we consider is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values (willingness to pay) placed by consumers on a public good such as endangered species. Sample consumers are asked whether they favor a referendum that would provide the good at a cost specified by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem under both nonparametric and semiparametric specifications.