Varinaccuracy of ranked set sample

Document Type : Original Article

Authors

• Manoj Chacko ¹
• Varghese George ²

¹ Department of Statistics, University of Kerala, Trivandrum, India

² Department of Statistics‎, ‎St‎. ‎Stephen's College‎, ‎Pathanapuram‎, ‎ ‎India‎

10.22067/smps.2024.45946

Abstract

In this paper‎, ‎Kerridge's inaccuracy measure and varinaccuracy of the ranked set sample (RSS) are considered‎. ‎By deriving the expression for Kerridge's inaccuracy measure and varinaccuracy of the r-th order statistic‎, ‎the expression for Kerridge's inaccuracy measure and varinaccuracy of RSS are obtained‎. ‎Kerridge's inaccuracy measure and varinaccuracy of moving ranked set sample are also obtained‎.

Keywords

• Inaccuracy measure
• Order statistics
• Ranked set sampling
• Varinaccuracy

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References

1.  Ahmadi, J. (2021). Characterization of continuous symmetric distributions using information measures of records. Statistical Papers, 62, 2603–2626.
2. Al-Odat, M. T., and Al-Saleh, M. F. (2001). A variation of ranked set sampling. Journal of Applied Statistical Science, 10, 137–146. 
3. Balakrishnan, N., Buono, F., Calì, C., and Longobardi, M. (2024). Dispersion indices based on Kerridge inaccuracy measure and Kullback-Leibler divergence. Communications in StatisticsTheory and Methods, 53, 5574–5592.
4. Buono, F., Calì, C., and Longobardi, M. (2021). Dispersion indices based on Kerridge inaccuracy and Kullback-Leibler divergence. arXiv preprint arXiv:2106. 12292.
5. Chacko, M., and George, V. (2023). Extropy properties of ranked set sample for Cambanis type bivariate distributions. Journal of the Indian Society for Probability and Statistics, 24, 111–133.
6.  Chacko, M., and George, V. (2024). Extropy properties of ranked set sample when ranking is not perfect. Communications in Statistics-Theory and Methods, 53, 3187–3210.
7. Chen, Z., Bai, Z., and Sinha, B. K. (2004). Ranked Set Sampling: Theory and Applications (Vol. 176). Springer, New York.
8. George, V., and Chacko, M. (2023). Cumulative residual extropy properties of ranked set sample for Cambanis type bivariate distributions. Journal of the Kerala Statistical Association, 33, 50–70.
9. Ghosh, A., and Kundu, C. (2018). On generalized conditional cumulative past inaccuracy measure. Applications of Mathematics, 63, 167–193.
10. Goel, R., Taneja, H. C., and Kumar, V. (2018). Kerridge measure of inaccuracy for record statistics. Journal of Information and Optimization Sciences, 39, 1149–1161.
11. Kayal, S., and Sunoj, S. M. (2017). Generalized Kerridge’s inaccuracy measure for conditionally specifid models. Communications in Statistics-Theory and Methods, 46, 8257–8268.
12. Kerridge, D. F. (1961). Inaccuracy and inference. Journal of the Royal Statistical Society. Series B (Methodological), 184–194.
13. McIntyre, G. A. (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3, 385–390.
14. Mohamed, M. S. (2019). A measure of inaccuracy in concomitants of ordered random variables under Farlie-Gumbel-Morgenstern family. Filomat, 33, 4931–4942.
15.   Mohammadi, M., Hashempour, M. (2023). Extropy based inaccuracy measure in order statistics. Statistics, 57, 1490–1510.
16. Nath, P. (1968). Inaccuracy and coding theory. Metrika, 13, 123–135. Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27, 379–423.
17. Sharma, A., and Kundu, C. (2024). Residual and past varinaccuracy measures. IMA Journal of Mathematical Control and Information, 41, 539–563.
18. Taneja, H. C., Kumar, V., and Srivastava, R. (2009). A dynamic measure of inaccuracy between two residual lifetime distributions. International Mathematical Forum, 4, 1213–1220.
19. Taneja, H. C., and Tuteja, R. K. (1986). Characterization of a quantitative-qualitative measure of inaccuracy. Kybernetika, 22, 393–402.
20. Thapliyal, R., and Taneja, H. C. (2013). A measure of inaccuracy in order statistics. Journal of Statistical Theory and Applications, 12, 200–207.
21. Thapliyal, R., and Taneja, H. C. (2015). On residual inaccuracy of order statistics. Statistics and Probability Letters, 97, 125–131.