New Bayesian Estimators for Randomized Response Technique

Abstract

This paper proposes new Bayesian estimators of the population proportion of a sensitive attribute when life data were collected through the administration of questionnaires on abortion on 300 matured women in some selected hospitals in Akure, Ondo State, Nigeria. Assuming both the Kumaraswamy (KUMA) and the generalised (GLS) beta distributions as alternative beta priors, efficiency of the proposed Bayesian estimators was established for a wide interval of the values of the population proportion (π). We observed that for small, medium as well as large sample sizes, the developed Bayesian estimators were better in capturing responses from respondents than the conventional simple beta estimator proposed by Hussain and Shabbir (2009a) as π approaches one.