In Gupta et al. (2010;2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a "three-stage optional randomized response model," a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresponding two-stage model, and with a smaller value of T. Greater respondent cooperation will be an added advantage of the three-stage model.

Auxiliary information is commonly used in sample surveys in order to achieve higher precision in the estimates. In this article we are concerned with the utilization of auxiliary information in the estimation stage in simple random sampling without replacement (SRSWOR), making use of an optional randomized response model proposed by Gupta et al. (2010). The underlying assumption is that the primary variable is sensitive in nature but a nonsensitive auxiliary variable exists that is positively correlated with the primary variable. We propose a ratio estimator of finite population mean and call it the additive ratio estimator. Expressions for the bias and mean square error of the proposed estimator are obtained to first order of approximation. Efficiency comparisons with the ordinary optional randomized response technique (RRT) mean estimator of Gupta et al. (2010) are carried out both theoretically and numerically. A simulation study is presented to evaluate the performance of the proposed estimator.

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Many kinds of errors in coding theory have been dealt with for which codes have been constructed to combat such errors. Though there is a long history concerning the growth of the subject and many of the codes developed have found applications in numerous areas of practical interest, one of the areas of practical importance in which a parallel growth of the subject took place is that of burst error detecting and correcting codes. The nature of burst errors differ from channel to channel depending upon the behaviour of channels or the kind of errors which occur during the process of data transmission. In very busy communication channels, errors repeat themselves more frequently. In view of this, it is desirable to consider repeated burst errors. The paper presents lower and upper bounds on the number of parity-check digits required for a linear code correcting errors in the form of repeated bursts. An upper bound for a code that detects m-repeated bursts has also been derived. Illustrations of several codes that correct 2-repeated bursts of different lengths have also been given.

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This paper deals with derivation of bounds for linear codes that are able to detect and locate errors which occur during the process of transmission. The kind of errors considered are known as repeated burst errors. An illustration for such kind of a code has also been provided.