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

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Abstract

Cost-effective sampling design is a problem of major concern in some experiments, especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In the current paper, the Fisher information matrix of the log-extended exponential–geometric distribution LEEGD\((\alpha ,\beta )\) with parameters \(\alpha \) and \(\beta \) based on simple random sample, ranked set sample (RSS), median RSS (MRSS) and extreme RSS is discussed. We obtain the expressions for the Fisher information matrix in each case and use them to perform efficiency comparisons. It is found that MRSS is most efficient when one parameter is inferred at a time (with the other parameter known), while RSS is most efficient when both parameters are inferred simultaneously. A real data set is used for illustration.

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Notes

  1. https://instruction.bus.wisc.edu/jfrees/jfreesbooks/Regression%20Modeling/BookWebDec2010/data.html, filename: RiskSurvey.

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Acknowledgements

The authors thank the Editor in Chief, an associate editor and reviewers for their valuable comments and suggestions to improve the paper. This research was supported by the National Science Foundation of China (Grant No. 11901236), Scientific Research Fund of Hunan Provincial Science and Technology Department (Grant No. 2019JJ50479), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 18B322), Winning Bid Project of Hunan Province for the 4th National Economic Census (Grant No. [2020]1), Young Core Teacher Foundation of Hunan Province (No. [2020]43) and Fundamental Research Fund of Xiangxi Autonomous Prefecture (Grant No. 2018SF5026).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Jishou University, Jishou, 416000, China

    Rui Yang, Wangxue Chen, Dongsen Yao, Chunxian Long, Yanfei Dong & Bingliang Shen

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  1. Rui Yang
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  2. Wangxue Chen
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  3. Dongsen Yao
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  4. Chunxian Long
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  5. Yanfei Dong
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Correspondence to Wangxue Chen.

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Yang, R., Chen, W., Yao, D. et al. The Efficiency of Ranked Set Sampling Design for Parameter Estimation for the Log-Extended Exponential–Geometric Distribution. Iran J Sci Technol Trans Sci 44, 497–507 (2020). https://doi.org/10.1007/s40995-020-00855-x

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