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In recent decades, many research studies have been conducted for the development of some new modifications of different baseline distributions to cope with real-world problems. This paper proposes a novel generalization of probability distributions, called modified type- II half-logistic distribution. We have derived the new family of probability distributions using T-X family with input as a type II variant of the half-logistic distribution. For the purpose of demonstration, the Weibull distribution is considered as a sub-model. Various algebraic properties of the suggested distribution have been discussed. For efficient parameter estimation, we have used the maximum likelihood principle. Additionally, two real-world data sets from the literature have been considered to illustrate the practical usefulness and significance of the suggested model.

In recent decades, the randomized response technique has attracted researchers due to its usefulness in sensitive surveys. The randomized response procedure is used for the collection of responses on sensitive issues such as cheating in examination, income earned through illegal sources, expenditure on luxury items, and amount of tax paid, etc. This study introduces a new variant of quantitative randomized response models for use with sample surveys where the variable of interest is quantitative. The properties of a mean estimator based on the new technique have been studied. Further, the combined and separate evaluation metrics for efficiency and privacy level have also been derived and compared with those of the existing methods. Further, a simulation study has been conducted to prove the improvement in the degree of privacy protection and efficiency. The findings reveal that the suggested randomized response technique is not only more efficient than the existing techniques, but also improves the joint measure of efficiency and respondents’ privacy, making it preferable over the existing techniques. A real-world example of a sample survey through the suggested model is also presented which illustrates its usefulness in practical surveys on sensitive issues.

In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.

In survey sampling, systematic sampling design has attracted survey researchers in recent years due to its simplicity of use. We introduce a modified variant of systematic sampling scheme which improves the efficiency of a recently developed diagonal systematic sampling method. The suggested modification is also found to be more efficient than the other popular sampling designs in circumstances where the units of the population under consideration exhibit an increasing or decreasing perfect or near-perfect linear trend. Moreover, it is observed that the conditions for efficiency are mathematically strong and practically always hold, hence making the suggested sampling design preferable over the available sampling designs.