There have been many alternative strategies for implementing sampling survey on quantitative characteristic of sensitive issues by using randomized response (RR) technique. The efficiency of most of those strategies has been improved by choosing the suitable design parameters of model. However, the two different procedures with pre-assigned design parameter values cannot ensure that they possess the same protection degree to the respondents. Some earlier comparisons of those strategies are inadequate (as in Eichhorn and Hayre, 1983 Eichhorn , B. H. , Hayre , L. S. ( 1983 ). Scrambled randomized response methods for obtaining sensitive quantitative data . J. Statist. Plann. Infer. 7 : 307 – 316 . [Crossref], [Web of Science ®] [Google Scholar] ; Gupta et al., 2002 Gupta , S. , Gupta , B. , Singh , S. ( 2002 ). Estimation of sensitivity level of personal interview survey questions . J. Statist. Plann. Infer. 100 ( 2 ): 239 – 247 . [Crossref], [Web of Science ®] [Google Scholar] ). Some literature contains a more comprehensive comparison based on efficiency and protection degree to the respondents among the qualitative characteristic RR techniques (see Bhargava and Singh, 2002 Bhargava , M. , Singh , R. ( 2002 ). On the efficiency comparison of certain randomized response strategies . Metrika 55 : 191 – 197 . [Crossref], [Web of Science ®] [Google Scholar] ; Nayak, 1994 Nayak , T. K. ( 1994 ). On randomized response surveys for estimating a proportion . Commun. Statist. Theor. Meth. 23 ( 11 ): 3303 – 3321 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ; Zaizai and Zankan, 2004 Zaizai , Y. , Zankan , N. ( 2004 ). A fair comparison of the randomized response strategies . Acta Mathematica Scientia 24A ( 3 ): 362 – 368 . [Google Scholar] ). As far as the comparisons are concerned that are based on efficiency and protection degree to the respondents among the quantitative characteristic RR techniques, very few related studies have been found so far. The purpose of this article is to give a more adequate comparison among those earlier quantitative characteristic RR strategies. It is found that several important differences between the results obtained in this article and some known results exist. Therefore, these earlier RR strategies should be reevaluated.

In this paper, the discrete extended Weibull distribution is introduced by discretizing a new extended the continuous Weibull distribution. The new model has decreasing, increasing, constant and upside-down bathtub shaped hazard rates. Some of basic distributional and reliability properties are studied. The maximum likelihood method is used to estimate the parameters of the model. The performance of the estimation method is evaluated by a Monte-Carlo simulation. Four-real life data sets are considered for illustrating the advantages of the proposed distribution over some other well-known discrete distributions.

This paper deals with Bayesian estimation and prediction for the inverse Weibull distribution with shape parameter α and scale parameter λ under general progressive censoring. We prove that the posterior conditional density functions of α and λ are both log-concave based on the assumption that λ has a gamma prior distribution and α follows a prior distribution with log-concave density. Then, we present the Gibbs sampling strategy to estimate under squared-error loss any function of the unknown parameter vector (α, λ) and find credible intervals, as well as to obtain prediction intervals for future order statistics. Monte Carlo simulations are given to compare the performance of Bayesian estimators derived via Gibbs sampling with the corresponding maximum likelihood estimators, and a real data analysis is discussed in order to illustrate the proposed procedure. Finally, we extend the developed methodology to other two-parameter distributions, including the Weibull, Burr type XII, and flexible Weibull distributions, and also to general progressive hybrid censoring.