In this paper, single-phase mixture regression cum ratio estimators are presented by utilizing auxiliary variables and auxiliary attributes simultaneously under stratified random sampling. Special cases of these estimators are discussed and further mean square errors are extracted mathematically. Also, to observe the properties of proposed estimators, simulation technique is used which shows that the distribution of the proposed estimators is approximately normal. To differentiate the performance of the proposed estimators, an empirical study has been conducted by incorporating quantitative and qualitative characteristics in the form of auxiliary attributes and variables simultaneously. Comparisons are made with single-phase mixture regression cum ratio estimators under simple random sampling. It has been found that the mixture regression cum ratio estimators employing multiple auxiliary variables and attributes, simultaneously, under stratified random sampling are more efficient than mixture regression cum ratio estimator under simple random sampling.

Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under Rank set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized family of estimators to estimate finite population mean of study variable under ranked set sampling utilizing information on an auxiliary variable. Bias and Mean Square Error (MSE) of the proposed generalized family of estimators are derived. The conditions of efficiency of proposed generalized family of estimators from competitor estimators are also derived. The applications of estimator are discussed using simulation study and real-life data sets for comparisons of efficiency. It is concluded that when correlation between study and auxiliary variables increases, the proposed generalized family of estimators proves to be the efficient estimator of population mean of the study variable.

In the contemporary era of information technology, copious amounts of data are ubiquitous, generated across various sectors on a daily basis. Analyzing every unit of data is impractical due to constraints such as limited resources in terms of time, labor, and cost. In such scenarios, survey sampling becomes a recommended approach for extracting information about population parameters. The primary goal of this study is to devise an estimation method for acquiring information about population parameters. We propose an optimal estimator for an improved estimation of the population mean in stratified random sampling by leveraging the information from two auxiliary attributes. The proposed estimator's bias, mean squared error (MSE), and minimum mean squared error are determined up to the first-order approximation. It is demonstrated that, under the derived conditions, the proposed estimator theoretically outperforms existing estimators. Four population are utilized to evaluate both the performance and applicability of the proposed estimator. The percentage relative efficiency (PRE) of proposed estimator for all the populations is 178.389, 142.881, 181.383, and 152.679 respectively. The suggested estimator superior to existing estimators, as demonstrated by the numerical examples.

Extreme-cum-median ranked set sampling has been developed to address the problem of heterogeneity and outliers / extreme values. Double ranked set sampling has been suggested to obtain more reliable samples using the concept of degree of distinguishability. Dealing with heterogeneous and non-normal populations seems to be an area with a dearth of research. This article endeavors to address this research gap by introducing a new, improved ranked set sampling procedure that combines the aforementioned approaches, which is called double extreme-cum-median ranked set sampling. A simulation study for some symmetric and asymmetric probability distributions has been conducted. The results show that the newly proposed scheme performs better than its competitors under perfect and imperfect ranking, but the best performance has been observed for Weibull distribution with perfect ranking. An empirical study utilizing real-life data following skewed distribution was carried out. The real-life data results align well with the Monte Carlo simulation outcomes. Due to its flexible ranking options, the newly proposed technique is suggested for heterogeneous and non-normal populations.

This study proposes a novel variance estimator \({\widehat{S}}_{Y,K}^{2}\)under two-phase sampling, utilizing one auxiliary variable and one binary attribute to enhance estimation efficiency. Theoretical properties of the estimator were obtained, such as the formula of bias and Mean Squared Error (MSE), which proves the analytical superiority of the estimator. The empirical efficiency of the simulation was demonstrated by the simulation performance in datasets of the health and education sectors, and the MSE values are consistently lower than those of the classical and competitive estimators. In further supporting its predictive power, machine learning classifiers (Regression Tree, Random Forest, and Support Vector Regression) were also trained on the same auxiliary inputs and evaluated benchmarked on the basis of Root Mean Squared Error (RMSE). Although Machine Learning (ML) models demonstrated good predictive power, the estimator used had good interpretability and theoretical foundations. Moreover, the three-parameter Weibull distribution was found to be the most suitable and cut-points were calculated to facilitate stratified interpretation of distributional analysis. In general, the research proves the usefulness of minimal auxiliary information as complemented by structured sampling and hybrid modeling to enhance precision of estimation of variance in applied studies.

1. Count data is found in many fields of life. Some examples include the number of heart attacks or hospitalization days in medical studies, the number of students absent during a period in educati...