Favourable Allocation Models for Symmetric Distributions   in Ranked Set Sampling

Neeraj Tiwari; Girish Chandra; Raman Nautiyal

doi:10.56093/jisas.v77i01.171569

Authors

Neeraj Tiwari Soban Singh Jeena University, Almora
Girish Chandra University of Allahabad, Prayagraj
Raman Nautiyal Soban Singh Jeena University, Almora

https://doi.org/10.56093/jisas.v77i01.171569

Keywords:

KPT model; Neyman’s allocation; Order statistic; Ranked set sample; Relative precision; Symmetric distribution. 2020 AMS Mathematics Subject Classification: 62D05; 62G09; 94A20

Abstract

Kaur et al. (2000) suggested an optimal allocation model for symmetric distribution in ranked set sampling (RSS). This model is not much applicable due to its dependency upon extreme or mid order statistic only. In this paper, an attempt to make a “favourable” and near optimal allocation has been made by allocating each rank order at least once and considering the opposite behavior of Neyman allocation for symmetric distribution. The case of perfect ranking is considered. The utility of the proposed model in terms of relative precision has been shown for some symmetric distributions. Favourable model outperforms both for equal and Neyman’s allocations and quite close to the optimal model for each set size. The model will provide a practical approach in situations where RSS is likely to lead to an improvement over simple random sampling and the underlying distribution is symmetric.

Downloads

Download data is not yet available.

References

Bhoj, D. and Chandra, G. (2019). Simple unequal allocation procedure for ranked set sampling with skew distributions. Journal of Modern Applied Statistical Methods, 18(2), eP2811. doi: 10.22237/jmasm/1604189700.

Dell, T.R. and Clutter, J.L. (1972). Ranked set sampling theory with order statistics background. Biometrics, 28, 545–555.

Harter, H.L. and Balakrishnan, N. (1996). CRC handbook of tables for the use of order statistics in estimation. CRC Press, Boca Raton, New York.

Kaur, A., Patil, G.P. and Taillie, C. (1994). Unequal allocation models for ranked set sampling with skew distributions. Technical Report 94-0930, Center for Statistical Ecology and Environmental Statistics, Pennsylvania State University, University Park.

Kaur, A., Patil, G.P. and Taillie, C. (1997). Unequal allocation models for ranked set sampling with skew distributions. Biometrics, 53, 123-130.

Kaur, A., Patil, G.P. and Taillie, C. (2000). Optimal allocation models for symmetric distributions in ranked set sampling. Annals of the Institute of Statistical Mathematics, 52(2), 239-254.

McIntyre, G.A. (1952). A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, 3, 385-390p.

Shirahata, S. (1982). An extension of the ranked set sampling theory. Journal of Statistical Planning and Inference, 6, 65-72.

Tiwari, N. and Chandra, G. (2011). A systematic procedure for unequal allocation for skewed distributions in ranked set sampling. Journal of the Society of Agricultural Statistics, 65(3), 331-338.

Yanagawa, T. and Chen, S. (1980). The MG-procedure in ranked set sampling. Journal of Statistical Planning and Inference, 4, 33-44.