DefinePK

Research Objective

To propose and evaluate the efficiency of an exponentially ratio type estimator under Ranked Set Sampling (RSS) design, comparing it with existing estimators.

Methodology

The study derives mathematical expressions for the Mean Squared Error (MSE) and Bias of the proposed estimator and existing estimators under RSS. A family of estimators is also proposed. Efficiency is compared mathematically and through numerical illustrations using three real-life population datasets with varying correlation levels (high negative, moderate, and high positive).

Methodology Flowchart

                        graph TD
    A["Define Research Objective"] --> B["Develop Proposed Estimator"];
    B --> C["Derive Theoretical Expressions for MSE and Bias"];
    C --> D["Identify and Review Existing Estimators"];
    D --> E["Perform Mathematical Efficiency Comparison"];
    E --> F["Select Real-Life Population Datasets"];
    F --> G["Conduct Numerical Illustrations"];
    G --> H["Analyze and Compare Results"];
    H --> I["Draw Conclusions"];                    

Discussion

The paper introduces a new exponentially ratio type estimator and demonstrates its superiority over several existing ratio-type estimators under RSS. The theoretical derivations of bias and MSE are supported by numerical comparisons, highlighting the practical advantages of the proposed estimator and the RSS methodology. The study also shows that the proposed estimator can encompass some existing estimators as special cases.

Key Findings

The proposed exponentially ratio type estimator is found to be more efficient than all other existing estimators under RSS design across the tested datasets. The RSS design itself is shown to yield minimum MSEs compared to Simple Random Sampling (SRS).

Conclusion

The proposed exponentially ratio type estimator is highly efficient and preferable over its competitive estimators under Ranked Set Sampling. The RSS design is more efficient than SRS. The findings suggest that the proposed estimator offers a better practice for future statistical studies.

Fact Check

1. The paper proposes an "exponentially ratio type estimator." This is a specific type of statistical estimator.
2. The study uses three real-life population datasets for numerical comparison.
3. The paper concludes that the proposed estimator is more efficient than existing estimators under RSS.

Mind Map