Improved exponential type variance estimators for population utilizing supplementary information.

This paper contributes to the existing literature on variance estimators by utilizing supplementary information. The variance estimation problem of a finite population is a significant matter as sometimes, it is tough to control the variation. For this purpose, an optimum family of exponential variance estimators is suggested under simple random sampling. Moreover, different specific members of the proposed estimators are identified by incorporating various known characteristics of the supplementary variable in the suggested generalized class of estimators. The derivations for the expressions of bias as well as mean square error (MSE) of the proposed estimators are conducted. The suggested family of estimators is studied in different situations by using sets of real data and simulation studies for their performance. To evaluate the efficiency of the suggested estimators, R software is used for the analysis. The study compares the performance of the proposed estimators against the traditional estimators. The theoretical and numerical comparisons show that the estimators suggested in the study are superior in efficiency as compared to the existing estimators.

Improved exponential type mean estimators for non-response case using two concomitant variables in simple random sampling.

This paper addresses new exponential estimators for population mean in case of non-response on both the study and the concomitant variables using simple random sampling. The expressions for theoretical bias and mean square error of new estimators are derived up to first-order approximation and comparisons are made with the existing estimators. The proposed estimators are observed more efficient as compared to the considered estimators in the literature. For instance, the classical [4] unbiased estimator, the estimator of [9], and other existing estimators under the explained conditions. The theoretical results are supported numerically by using real-life data sets, under the criteria of bias, mean square error, percent relative efficiency and mathematical conditions. It is also clear from the numerical results that the suggested exponential estimators performed better than the estimators in the literature.

Evolution of basic human values orientations: An application of monitoring changes in cluster solutions.

This study enumerates the evolution of basic human values orientations and the dynamic relationship between them, computed from Schwartz's value survey conducted in European nations. For this purpose, eight datasets related to the human value scale were extracted from the European Social Survey; each corresponds to a single round conducted cross-sectionally every two years since 2001. Change detection algorithm was implemented to the cluster solutions of temporal datasets, and the evolution of important clusters was traced. Finding of the study reveals that Universalism and Benevolence values are on the rise in European societies in the last couple of decades. Most of the European inhabitants believe in the smooth group functioning and form the organismic needs of cooperation. The people prefer anxiety-free life, and love for nature, environment, humanity, and kindness to other beings in society are essential constructs for them. They avoid self-centred behaviour and prefer social physiognomies.