Improving Finite Population Mean through Ranked Sets

Authors

  • Poonam Singh Department of Statistics, Banaras Hindu University, Varanasi – 221005, India
  • Sooraj Gupta Department of Statistics, Banaras Hindu University, Varanasi – 221005, India
  • Pooja Maurya Department of Statistics, Banaras Hindu University, Varanasi – 221005, India
  • Prayas Sharma Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India

DOI:

https://doi.org/10.13052/jrss0974-8024.1924

Keywords:

Ratio-type exponential estimator;, Ranked Set Sampling, Log-type exponential estimator;, Bias, Simulations, Mean-squared error (MSE), Percentage relative efficiency (PRE)

Abstract

In the field of sampling theory, simple random sampling (SRS) has been widely used and proven to be effective for drawing samples to estimate population parameters. However, in certain situations, obtaining observations on the study variable is more challenging than ranking the units. In such cases, ranked set sampling (RSS) becomes very useful in the estimation of population parameters. We offer two new estimators under RSS to estimate the finite population mean out of which one estimator is equivalent to the many estimators existing in the literature, Therefore it can be used as the alternatives to the existing ones while the other one performs better than the recent estimator Khalid et al., (2024) in terms of mean squared error (MSE) and percentage relative efficiency (PRE), under RSS framework. Among the two proposed estimators, One of these estimators combines log and exponential, while the other combines regression and exponential.We found that second estimator turns out to be most efficient among the estimators studied in this study under RSS. The MSE and PRE are employed to evaluate the performance of the proposed estimators in comparison with traditional estimators discussed in this study. Analytical expressions for the MSE and bias are derived, along with the conditions under the proposed estimators demonstrate improved efficiency. To substantiate the theoretical findings, both empirical and simulation studies are conducted. The results indicate that the proposed estimators provide better performance compared to traditional estimators.

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Author Biographies

Poonam Singh, Department of Statistics, Banaras Hindu University, Varanasi – 221005, India

Poonam Singh is an Assistant Professor in the Department of Statistics, Institute of Science, at Banaras Hindu University. She obtained her B.Sc. (Hons.), M.Sc., and Ph.D. in Statistics from Banaras Hindu University and served as a Visiting Fellow at University of Technology Sydney in 2025. Her research interests include sampling theory, applied statistics, neutrosophic theory, and machine learning. Dr. Singh has published numerous research articles in reputed international journals indexed in SCIE, ESCI, and Scopus, and has authored a scholarly book on survey sampling. She has successfully supervised postgraduate research and is currently guiding doctoral scholars. She is a recipient of the Global Experience Faculty Program Fellowship and the Institute of Eminence (IoE) Research Grant from BHU. Dr. Singh actively serves as a reviewer for several international journals and is a member of professional organizations including the Indian Society of Probability and Statistics, the Epidemiology Foundation of India, and the Indian Bayesian Society.

Sooraj Gupta, Department of Statistics, Banaras Hindu University, Varanasi – 221005, India

Sooraj Gupta is a Research Scholar in the Department of Statistics at Banaras Hindu University. He completed his Bachelor’s and Master’s degrees in Statistics from the same institution with distinction. His doctoral research focuses on the development of efficient estimators for finite population parameters using auxiliary information in survey sampling. His research interests include survey sampling, ranked set sampling, estimation theory, and statistical applications in agriculture and socio-economic studies. He has published research in internationally indexed journals, including Neutrosophic Sets and Systems and REVSTAT–Statistical Journal. He is proficient in R, Python, SPSS, and statistical computing tools, and has qualified national-level examinations such as JAM and GATE in Statistics.

Pooja Maurya, Department of Statistics, Banaras Hindu University, Varanasi – 221005, India

Pooja Maurya is a Research Scholar in the Department of Statistics at Banaras Hindu University, where she is pursuing her Ph.D. under the supervision of Dr. Poonam Singh. She obtained her M.Sc. in Statistics from Banaras Hindu University with a CGPA of 9.11 and her B.Sc. in Mathematics, Statistics, and Computer Science from Deen Dayal Upadhyaya Gorakhpur University. Her research interests lie in sampling theory, particularly in developing efficient estimators for population parameters using auxiliary information in time-scaled surveys. She has authored several publications in internationally indexed journals and has served as a reviewer for leading statistical journals. Her expertise includes statistical computing and data analysis using R, Python, MATLAB, Stata, and LaTeX.

Prayas Sharma, Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India

Prayas Sharma is an Assistant Professor in the Department of Statistics, School of Physical and Decision Science, at Babasaheb Bhimrao Ambedkar University. He earned his Ph.D. in Statistics from Banaras Hindu University and has over 12 years of teaching and 13 years of research experience. His research interests include sampling theory, predictive modeling, business analytics, artificial intelligence and machine learning, applied statistics, and energy sustainability. Dr. Sharma has authored more than 50 research papers in reputed international journals indexed in SCIE, ESCI, Scopus, and ABDC databases, along with a book and several book chapters. He serves on the editorial boards of several international journals and actively reviews manuscripts for leading statistical and interdisciplinary journals. He is a member of professional bodies including the International Indian Statistical Association (IISA) and the Indian Society for Probability and Statistics (ISPS).

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Published

2026-06-16

How to Cite

Singh, P. ., Gupta, S. ., Maurya, P. ., & Sharma, P. . (2026). Improving Finite Population Mean through Ranked Sets. Journal of Reliability and Statistical Studies, 19(02), 311–346. https://doi.org/10.13052/jrss0974-8024.1924

Issue

2026: Vol 19 Iss 2

Section

Articles