The Efficiency of Ranked Set Sampling Design for Parameter Estimation for the Log-Extended Exponential–Geometric Distribution

Estimation methods based on ranked set sampling for the power logarithmic distribution

The sample strategy employed in statistical parameter estimation issues has a major impact on the accuracy of the parameter estimates. Ranked set sampling (RSS) is a highly helpful technique for gathering data when it is difficult or impossible to quantify the units in a population. A bounded power logarithmic distribution (PLD) has been proposed recently, and it may be used to describe many real-world bounded data sets. In the current work, the three parameters of the PLD are estimated using the RSS technique. A number of conventional estimators using maximum likelihood, minimum spacing absolute log-distance, minimum spacing square distance, Anderson-Darling, minimum spacing absolute distance, maximum product of spacings, least squares, Cramer-von-Mises, minimum spacing square log distance, and minimum spacing Linex distance are investigated. The different estimates via RSS are compared with their simple random sampling (SRS) counterparts. We found that the maximum product spacing estimate appears to be the best option based on our simulation results for the SRS and RSS data sets. Estimates generated from SRS data sets are less efficient than those derived from RSS data sets. The usefulness of the RSS estimators is also investigated by means of a real data example.

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.

An improved version of systematic sampling design for use with linear trend data

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.