Improved estimation of the sensitive proportion using a new randomization technique and the Horvitz–Thompson type estimator

Randomized response techniques efficiently collect data on sensitive subjects to protect individual privacy. This paper aims to introduce a new randomizing technique in the additive scrambled model so that privacy is well preserved and the estimator's efficiency for the sensitive population proportion is improved. Also, a Horvitz–Thompson type estimator is presented as an unbiased estimator of the sensitive proportion of the population, then convergence to the normal distribution for the Horvitz–Thompson type estimator is considered by the entropy of the inclusion indicators in the Poisson sampling. Eventually, using the new additive scrambled model, the ratio of taking addictive drugs is estimated among students of the University.