Auxiliary information plays a vital role in parameter selection and estimation to achieve efficient estimates of unknown population parameters. Dual use of auxiliary information, i. e., \original" and \ranked" auxiliary variables, helps increase the e, ciency of estimators. In this paper, the performance of di, erence-type-exponential estimators was proposed and evaluated based on dual auxiliary information for population mean under SIMPLE RANDOM SAMPLING. Mathematical expressions for the bias and the mean squared error of the proposed estimators were obtained. Three real-life data sets and Monte Carlo simulation studies were carried out for illustration. The results of empirical and simulation studies indicate that the proposed estimators outperformed their counterparts in terms of mean square errors and percentage relative efficiency.

Auxiliary information plays a vital role at the selection and/or estimation stage to achieve the efficient estimates of the unknown population parameters. Dual use of auxiliary information, one the original and second the ranks of the auxiliary variable help to increase the efficiency of the estimators. In this article, we proposed and evaluated the performance of difference-type-exponential estimators based on dual auxiliary information for population mean under SIMPLE RANDOM SAMPLING. Mathematical expressions for the bias and the mean squared error of the proposed estimators are obtained. Three real-life data sets and Monte Carlo simulation studies are carried out for illustration. The results of the empirical and the simulation studies, in terms of mean square errors and percentage relative efficiencies indicate that the proposed estimators perform better as compared to their counterparts.

This study proposes optional RANDOMized Response Technique (RRT) models in a binary response situation. The application of the proposed optional RRT models under strati cation is also explored. Gupta et al. [1] introduced an ingenious idea of optional RRT model in which a question may appear sensitive to one respondent while being not sensitive to another. This study focuses on estimating  , the prevalence of sensitive attribute,! , the sensitivity level of the underlying sensitive question when the proportion of unrelated innocuous attribute  x is unknown. A new multi-question approach is proposed for estimation of parameters ( ; ! ). A comparison between the proposed optional RRT models and the corresponding full RRT models is carried out numerically under SIMPLE and strati ed RANDOM SAMPLING.

This paper introduces a new two-stage RANDOMized response model for estimating the mean of a sensitive quantitative RANDOM variable. The proposed model is obtained for both SIMPLE and stratified RANDOM SAMPLING. The efficiency of the proposed estimator, under both SAMPLING schemes, is investigated with respect to various estimators and it is found to be more efficient. Moreover, a new measure for evaluating the performance of any RANDOMized response estimator is introduced. The measure considers the relative efficiency of the RANDOMized response estimator, and the privacy protection it offers. The performance of the proposed estimator is examined using the new measure and it is found to have an overall better performance than its rival estimators. A real data example is also examined using the proposed model and various models from literature.

In this paper, we have proposed an estimator of finite population mean in stratified RANDOM SAMPLING. The expressions for the bias and mean square error of the proposed estimator are obtained up to the first order of approximation. It is found that the proposed estimator is more efficient than the traditional mean, ratio, exponential, regression, Shabbir and Gupta (in Commun Stat Theory Method 40: 199– 212, 2011) and Khan et al. (in Pak J Stat 31: 353– 362, 2015) estimators. We have utilized four natural and four artificial data sets under stratified RANDOM SAMPLING scheme for assessing the performance of all the estimators considered here.

One of the most important information in urban forestry is the knowledge of their areas. Nowadays, for this purpose, different methods are used in different countries. In tis research, the firest one carried out in Iran, different SAMPLING methods including 100% inventory with 10-meters strips, SIMPLE RANDOM SAMPLING, RANDOMized block SAMPLING, systematic RANDOM SAMPLING, two stage SAMPLING and dot grid SAMPLING using the aerial photographs, were used to obtain the areas covered by street trees. The study area was valieasr Avenue in Tehran (right and left side of 5000 meters of the avenue with 500 transects). The largest length of tree s crown (Which is the same as strip s width that were at the beginning point of any strip or the nearest) were measured by 100% inventory (the comparison base for other methods). Strip s areas were calculated using the largest crown length for each method 50 strips were selected and the measurements were carried out and analyzed. Normality of data were tested by x2-test and t-test was used to determine the difference only block RANDOM SAMPLING had difference between each different SAMPLING had difference, there for T× E2% value was calculated for other methods. Results showed that dot grid SAMPLING is the best inventory method in urban forestry.

Introduction: In some biological, environmental or ecological studies, there are situations in which obtaining exact measurements of sample units are much harder than ranking them in a set of small size without referring to their precise values. In these situations, ranked set SAMPLING (RSS), proposed by McIntyre (1952), can be regarded as an alternative to the usual SIMPLE RANDOM SAMPLING (SRS) to draw a more representative sample from the population of interest than what is possible in SRS. To draw a ranked set sample, one first draws n SIMPLE RANDOM samples, each of size n, from the population of interest and ranks them in an increasing magnitude. The ranking process is done without measuring sample units and therefore it need not to be accurate. One then identifies the ith sample unit from the ith sample for actual quantification (for i=1, … , n). Finally, he repeats this process m times (cycle) if he/she is required to obtain a sample of size mn. Since a ranked set sample contains information from both measured sample units and their corresponding ranks, one intuitively expects that statistical inference based on RSS to be more accurate than what is possible to obtain based on SRS. This paper is concerned with problem of estimating variance of the normal distribution in RSS. Several methods of estimation of variance of the normal distribution are described and compared via a Monte Carlo simulation study. Material and methods: All simulation studies in this paper have been done using R statistical software version R-3. 3. 1 Results and discussion: In this paper, we consider estimation of the normal variance based on a ranked set sample with single (multiple) cycle(s) and propose different unbiased estimators for each case. Our simulation results indicate that the mean square error (MSE) of each estimator is decreased as the values of n or m increases while the other parameters are kept fixed. It is also found that the estimator based on combining variance estimators of within and between ranking classes has typically better performance than the others. Conclusion: The following results can be obtained based on our simulation study: If there is a single cycle in RSS, then the proposed estimator in the case of single cycle beats Stokes-modified unbiased estimator. In the multiple cycle case in RSS, the estimator based on combining variance estimators of within and between ranking classes is the best one.

In the estimation of a probability density function (PDF) by kernel method, two inherent problems are the choice of SAMPLING methods and the selection of a bandwidth. In this article, we use the balanced and unbalanced ranked set SAMPLING (RSS) methods and Bayesian bandwidth to estimate a PDF by kernel method. To compare our method with existing methods, we use an extensive simulation study to compare the RSS with SIMPLE RANDOM SAMPLING (SRS) PDF estimator and also Bayesian bandwidth with other existing bandwidths. As an application, we use the household expenses and income data of the Statistical Center of Iran in 2021 to estimate the PDF of the total expenses of the households in Tehran province.

Traditional Ordinary Least Square (OLS) regression is commonly utilized to develop regression-ratio-type estimators through traditional measurement of location. Abid et al. [Abid, M., Abbas, N., Zafar Nazir, H., et al. \Enhancing the mean ratio estimators for estimating population mean using non-conventional location parameters", Revista Colombiana de Estadistica, 39(1), pp. 63{79 (2016b)], extended this idea and developed regression-ratio-type estimators based on traditional and non-traditional measures of location. In this article, the quantile regression with traditional and non-traditional measures of location is utilized and a class of ratio type mean estimators is proposed. The theoretical Mean Square Error (MSE) expressions are also derived. The work is also extended to two-phase SAMPLING (partial information). The relationship between the proposed and existing groups of estimators is shown by considering real data collections originating from different sources. The discoveries are empowering and prevalent execution of the proposed group of the estimators is witnessed and documented throughout the article.