Novel randomized response method for mean estimation using exponential estimators

.In applied research, the objective of the study often involves topics of a sensitive nature. When the research objective has such characteristics, using direct questioning methods in sampling typically does not yield reliable results. This is because respondents may either refuse to answer or provide responses that may deviate significantly from the truth. To address this issue, random response techniques are employed. This method reduces non response bias and leads to more reliable estimates. In this article, we introduce a novel three-mode randomized response method and demonstrate its superiority through simulation studies. Furthermore, we develop exponential-type estimators using auxiliary information to improve the estimation of the mean of the sensitive variable. We show that under certain conditions, these estimators outperform the classical version. As a practical application, we refine the estimation of the average level of academic dishonesty among students at Shahid Chamran University of Ahvaz using the proposed exponential-type estimators.