A simple way of improving the Bar–Lev, Bobovitch and Boukai Randomized response model


  • Tanveer A. Tarray Department of Mathematics, Islamic University of Science and Technology-Awantipora- Pulwama- Kashmir- India-192122
  • Housila P. Singh School of Studies in Statistics, Vikram University Ujjain - M.P.- India-456010


Estimation of proportion, randomized response sampling, respondents protection, sensitive quantitative variable.


Eichhorn & Hayre (1983) considered a randomized response procedure suitable for estimating the mean response, when the sensitive variable under investigation is quantitative in nature. They have obtained an estimate for the mean of the quantitative response variable under investigation and studied its properties. Bar–Lev et al. (2004) have suggested an alternative procedure, which use a design parameter (controlled by the experimenter) that generalizes Eichhorn & Hayre’s (1983) results. They have also proved that the estimator proposed by them has uniformly smaller variance as compared to that of Eichhorn & Hayre (1983) in certain condition. In this paper we have suggested a simple procedure of improving the Eichhorn & Hayre (1983) and Bar–Lev et al. (2004) models along with its properties. It has been shown that the proposed procedure is uniformly better than Bar–Lev et al. (2004) procedure. The proposed procedure is also uniformly better than Eichhorn and Hayre’s (1983) procedure under the same condition in which the Bar–Lev et al.’s (2004) procedure is more efficient than Eichhorn & Hayre’s (1983) procedure. Numerical illustration is given in support of the present study.

Author Biography

Tanveer A. Tarray, Department of Mathematics, Islamic University of Science and Technology-Awantipora- Pulwama- Kashmir- India-192122

Department of Mathematics, Islamic University of Science and Technology-Awantipora- Pulwama- Kashmir- India-192122 - Assistant Professor


Chaudhuri, A. & Mukerjee, R. (1988). Randomized

response: Theory and techniques. Marcel- Dekker, New

York, USA.

Bar –Lev,SKE., Bobovitch, E. & Boukai, B. (2004). A

note on randomized responsemodels for quantitative data.

Metrika, 60:225 -250.

Eichhorn, B.H. & Hayre, L.S. (1983). Scrambled

randomized response methods for obtaining sensitive

quantitative dada. Journal of Statistics and planning

Inference, 7:307 -316.

Fox, J.A. & Tracy, P.E. (1986). Randomized Response:

A method of Sensitive Surveys. Newbury Park, CA:

SEGE Publications.

Gjestvang, C.R. & Singh, S. (2006). A new randomized

response model. Journal of Royal Statistical Society, 68:


Gjestvang, C.R. & Singh, S. (2009). An improved

randomized response model: Estimation of mean,

Journal of Applied Statistics, 36(12): 1361 -1367.

Hussain, Z. (2012). Improvement of Gupta and

Thornton scrambling model through double use of

randomization device. International Journal of Academic

ResearchBusiness and Society and Science, 2(6),91 -97.

Odumade, O. & Singh, S. (2008). Generalized forced

quantitative randomized response model: A unified

approach. Journal of Indian Society of Agricultural and

Statistics, 62(3): 244 -252.

Odumade, O. & Singh, S. (2009). Improved Bar-Lev,

Bobovitch and Boukai randomized response models.

Communication in Statistics andTheory and .

Methods, 38(3):473 -502.

Singh, H.P. & Mathur, N. (2004). Estimation of

population mean with known coefficient of variation

under optional response model using scrambled response

technique.Statistics and Transactions, 6 (7):1079 -1093.

Singh, H.P. & Mathur, N. (2005). Estimation of

population mean when coefficient ofvariation is known

using scrambled response technique. Journal of

Statistics and Planning Inference, 131:135 -144.

Singh, H.P. & Tarray, T.A.(2013). A modified survey

technique for estimating the proportion and sensitivity in

a dichotomous finite population.International

Journal of Advanced Sciences and Technology Research,

(6):459 – 472.

Singh, H.P. & Tarray, T.A.(2016). An improved Bar –

Lev, Bobovitch and Boukai randomized response model

using moments ratios of scrambling variable.

Hacettepe Journal of Mathematics and Statistics,

(2):593 -608.

Singh, S. (2003). Advanced sampling theory with

applications. Kluwer Academic Publishers, Dordrecht,

The Netherlands.

Tarray, T.A. & Singh, H.P. (2015). Some improved

additive randomized response models utilizing higher

order moments ratios of scrambling variable. Model

Assisted Statistics and Applications, 10:361 -383.

Tarray, T.A. & Singh, H.P. (2016). An adroit randomized

response new additive scrambling model. Gazi University

Journal of Sciences, 29(1):159 -165.

Tarray, T.A. & Singh, H.P. (2017). A Survey Technique

for Estimating the Proportion and Sensitivity in a

Stratified Dichotomous Finite Population.

Statistics and Applications, 15(1,2):173 -191.

Warner, S.L. (1965). Randomized response: A survey

technique for eliminating evasive answer bias. Journal of

American Statistical Association, 60:63 -69.