Estimations on Rician Distribution Using Ranked Set Sampling
DOI:
https://doi.org/10.59992/IJESA.2025.v4n6p10Keywords:
Ranked Set Sampling, Simulation, Rician Distribution, Arithmetic Mean, Geometric Mean, Harmonic Mean, Quadratic Mean, Mean Deviation, Coefficient of Variation, Coefficient of Skewness, Coefficient of Kurtosis, Biasness, MSE and Relative EfficiencyAbstract
There are many situations where it is costly to measure the variable under the study, but this variable can be easily ranked. Ranked set sampling (RSS) utilizes the information of the ranks in addition to the measurements. It was proved that RSS is more efficient than simple random sampling (SRS) when estimating the population arithmetic mean for the same sample size. Because of its efficiency, RSS was employed to a wide range of applications and becoming an interesting method for many researchers. It was studied parametrically and non-parametrically and several estimators based on different statistical distributions were investigated. This research adopts Rician distribution and several measurements from this distribution were investigated based on RSS. The estimations include the arithmetic, geometric, harmonic, quadratic means as well as the median, variance, mean deviation, coefficient of variation, coefficient of skewness and kurtosis. Simulation study shows that the estimators based on RSS are more efficient than those based on SRS. However, the gain in the efficiency with variance and coefficient of kurtosis is not too much and even worse for small sample size.
References
1. Adatia, A. Estimation of parameters of the half-logistic distribution using generalized ranked set sampling. Computational Statistics and Data Analysis 2000, 33: 1-13.
2. Al-Hadhrami, Said Ali. Estimation of the Population Variance Using Ranked Set Sampling with Auxiliary Variable. The International Journal of Contemporary Mathematical Sciences 2010; no. 52, 2567 – 2576.
3. Al-Hadhrami, Said Ali. Parametric Estimation on Modified Weibull Distribution Based on Ranked Set Sampling. European Journal of Scientific Research 2010; volume 44 (1):73-78.
4. Al-Hadhrami, Said Ali. Generalization of Chain Ratio Type estimators. World Academy of Science, Engineering and Technology 2010; Volume 62: pp1036-1040.
5. Al-Hadhrami, Said Ali. Ratio Type Estimators of the Population Mean Based on Ranked Set Sampling. World Academy of Science, Engineering and Technology 2009; Volume 59: pp 360-364.
6. Al-Omari, A.I., Ibrahim, K., Jemain, A.A. and Al-Hadhrami, Said Ali. Multistage Balanced Groups Ranked Set Samples for Estimating the Population Median. Statistics in Transition 2009; vol.10, no. 2, pp. 223-233.
7. AL-Saleh, M.F., AL-Sharafat, K. and Muttlak, H. Bayesian estimation using ranked set sampling. Biometrical Journal 2000; 42, 489-500.
8. Arnold, B. C. and Groeneveld, R. A. Measuring Skewness with Respect to the Mode, The American Statistician 1995; 49, 34-38.
9. Balanda, K. P. and MacGillivray, H. L. Kurtosis: A Critical Review, the American Statistician 1988; 42, 111-119.
10. Bantan, R., Hassan, A Elsehetry, M. Zubair Lomax Distribution: Properties and Estimation Based on Ranked Set Sampling. Computers, Materials and Continua 2020; 65(3):2169-2187.
11. Behrens, T., & Joshi, S. A review of Rician channel models for biomedical applications. IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology 2013; 1(1), 24-30.
12. Cochran, W. G. Sampling techniques 1977; (3rd ed.). John Wiley & Sons.
13. Evans, M. J. Application of ranked set sampling to regeneration, Surveys in areas direct-seeded to long leaf pine, Master Thesis, school for Forestry and Wild-life Management, Louisiana state University, Baton Rouge, Louisiana.1967.
14. Fei, H., Sinha, B. and WU, Z. Estimation of parameters in two-parameter Weibull and extreme-value distributions using ranked set sampling. Journal of Statistical Research, 1994; 28, 149- 161.
15. Goldsmith, A. J. Wireless Communications. Cambridge: Cambridge University Press.2005.
16. Halls, L. S. and Dell, T. R. Trial of ranked set sampling for forage yields. Forest Science, 1966; 12, 22-26.
17. Hedayat, A. S., & Sinha, B. K. Design and inference in finite population sampling. John Wiley & Sons. 2005.
18. Joanes, Derrick N.; Gill, Christine A. Comparing measures of sample skewness and kurtosis, Journal of the Royal Statistical Society, Series D, 1998; 47 (1): 183–189.
19. Kaur, A., Patil, G.P. and Taillie, C. Unequal allocation models for ranked set sampling with skew distributions. Biometrics, 1997; 53, 123-130.
20. Kaur, A., Patil, G.P. and Taillie, C. Optimal allocation for symmetric distributions in ranked sampling. Annals of the Institute of Statistical Mathematics, 2000; 52, 239-254.
21. Lam, K., Sinha, B., and WU, Z. Estimation of parameters in a two-parameter exponential distribution using ranked set sampling. Annals of the Institute of Statistical Mathematics, 1994; 46, 723-736.
22. McIntyre, G.A. A Method for Unbiased Selective Sampling Using Ranked Sets. Australian Journal of Agricultural Research, 1952; 3, 385-390.
23. Melek & Selma. Parameter estimation of generalized Rayleigh distribution based on ranked set sample. Journal of Statistical Computation and Simulation, 2017, 88. Pages 615-628.
24. Poon, A. S. Y., & Zhang, Q. T. Wireless communication systems: from RF subsystems to 4G enabling technologies. Singapore: John Wiley & Sons. 2004.
25. Proakis, J. G. Digital Communications. New York: McGraw-Hill.1995.
26. Rappaport, T. S. Wireless Communications: Principles and Practice. New Jersey: Prentice Hall.2002.
27. Rice, S. O. Mathematical analysis of random noise. Bell System Technical Journal, 1944; 23(3), 282-332.
28. Samuh, Al-Omari and Nursel. Estimation of the parameters of the new Weibull-Pareto distribution using RSS. STATISTIC. 2020; 80, sa.1, ss.103-123.
29. Shen, W.H. On the estimation of lognormal mean using a ranked set sample. Sankhya, the Indian Journal of Statistics, 1994; 56, 323-333.
30. Sinha, B.K., Sinha, R.K. and Purkayastha, S. On some aspects of ranked set sampling for estimation of normal and exponential parameters. Statistical Decisions, 1996; 14, 223-240.
31. Stokes, S.L. Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 1995; 47, 465-482.
32. Takahasi, K K. and Wakimoto, K. On the unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 1968; 20, 1-31.
33. Thompson, S. K. Sampling (3rd ed.). John Wiley & Sons. 2012.
34. Westfall, Peter H. Kurtosis as Peakedness, 1905 - 2014. R.I.P., the American Statistician, 2014; 68 (3): 191–195.
35. Yerima, S. Y., & Sparkes, M. Rician and non-central chi-squared distributions: Applications in wireless communication and signal processing. IET Signal Processing, 2015; 9 (7), 538-547.
