Estimation of the Distribution Function of a Continuous Type Random Variable Through Randomized Response
In 1965 Stanley Warner  illustrated a technique whereby one could estimate from a sample the proportion of persons in a population possessing some characteristic $X$, without pointedly asking the question, 'Do you possess characteristic $X$?'. The present article uses a variation of these ideas suggested by Warner in a later paper  to estimate the distribution function of a continuous-type random variable. The technique is illustrated by estimating an income distribution from the responses of a sample of 500 individuals. The potential use of devices of this type in maintaining confidentiality of existing data files is apparent
Poole, W. (1974). Estimation of the Distribution Function of a Continuous Type Random Variable Through Randomized Response. Journal of the American Statistical Association, 69(348), 1002-1005.