Using the exponential function of scrambling variable in quantitative randomized response models

In sample surveys, refusals and untruthful reporting by the respondents are serious issues often faced by the researchers during the data collection process. Over the past few decades, randomized response models have gained wide popularity among survey statisticians as a tool to reduce the non-response rate. The existing literature on quantitative randomized response models utilize the scrambling variable either as an additive term or as a multiplicative factor. This paper introduces the novel idea of the use of the exponential function of scrambling variable in quantitative randomized response models. Two new quantitative randomized response models are proposed based on exponential scrambling variable. It is found that the new randomized response models are more efficient than the existing quantitative randomized response models. The mathematical properties of the mean estimator of the sensitive variable under the new proposed methods have been discussed. Moreover, the joint and separate measures of privacy protection and efficiency of the proposed and existing models have also been discussed. Further, to illustrate the practical implementation of the suggested models, an example of data collection is also presented.