© Amal S. Hassan, Rasha S. Elshaarawy, Heba F. Nagy. Article available under the CC BY-SA 4.0 licence
Partial ranked set sampling (PRSS) is a cost-effective sampling method. It is a combination of simple random sample (SRS) and ranked set sampling (RSS) designs. The PRSS method allows flexibility for the experimenter in selecting the sample when it is either difficult to rank the units within each set with full confidence or when experimental units are not available. In this article, we introduce and define the likelihood function of any probability distribution under the PRSS scheme. The performance of the maximum likelihood estimators is examined when the available data are assumed to have an exponentiated exponential (EE) distribution via some selective RSS schemes as well as SRS. The suggested ranked schemes include the PRSS, RSS, neoteric RSS (NRSS), and extreme RSS (ERSS). An intensive simulation study was conducted to compare and explore the behaviour of the proposed estimators. The study demonstrated that the maximum likelihood estimators via PRSS, NRSS, ERSS, and RSS schemes are more efficient than the corresponding estimators under SRS. A real data set is presented for illustrative purposes.
exponentiated exponential distribution, partial ranked set sampling, neoteric ranked set sampling, maximum likelihood method
Abu-Dayyeh, W., Assrhani, A., Ibrahim, K., (2013). Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling. Statistical Papers, 54(1), pp. 207–225.
Abu-Youssef, S. E., Mohammed, B. I., Sief, M. G., (2015). An extended exponentiated exponential distribution and its properties. International Journal of Computer Applications, 121(5), pp. 1–6.
Al-Odat, M. T., Al-Saleh, M. F., (2001). A variation of ranked set sampling. Journal of Applied Statistical Science, 10(2), pp. 137–146.
Al-Omari, A. I., Almanjahie, I. M., Hassan, A. S., Nagy, H. F., (2020). Estimation of the stress-strength reliability for exponentiated Pareto distribution using median and ranked set sampling methods. CMC-Computers, Materials & Continua, 64(2), pp. 835–857.
Almarashi, A. M., Algarni, A., Hassan, A. S., Elgarhy, M., Jamal, F., Chesneau, C., Alrashidi, K., Mashwani, W. K., Nagy, H. F., (2021). A new estimation study of the stress-strength reliability for the Topp–Leone distribution using advanced sampling methods. Scientific Programming, pp. 1–13, https://doi.org/10.1155/2021/2404997.
Bantan, R., Hassan, A. S., Elsehetry, M., (2020). Zubair Lomax distribution: properties and estimation based on ranked set sampling. CMC-Computers, Materials & Continua, 65(3), pp. 2169–2187.
Bhoj, D. S., Ahsanullah, M., (1996). Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, pp. 685–694.
Bjerkedal, T., (1960). Acquisition of resistance in Guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Hygiene, 72(1), pp. 130–148.
Chesneau, C., Kumar, V., Khetan, M., Arshad, M., (2022). On a modified weighted exponential distribution with applications. Mathematical and Computational Applications, 27(1), https://doi.org/10.3390/mca27010017.
De Andrade, T. A., Bourguignon, M., Cordeiro, G. M., (2016). The exponentiated generalized extended exponential distribution. Journal of Data Science, 14(3), pp. 393–413.
Gupta, R. D., Kundu, D., (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), pp. 173–188.
Gupta, R. D., Kundu, D., (2007). Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference, 137(11), pp. 3537–3547.
Haq, A., Brown, J., Moltchanova, E., Al-Omari, A. I., (2013). Partial ranked set sampling design. Environmetrics, 24(3), pp. 201–207.
Hassan, A. S., (2012). Modified goodness of fit tests for exponentiated Pareto distribution under selective ranked set sampling. Australian Journal of Basic and Applied Sciences, 6(1), pp. 173–189.
Hassan, A. S., (2013). Maximum likelihood and Bayes estimators of the unknown parameters for exponentiated exponential distribution using ranked set sampling. International Journal of Engineering Research and Applications, 3(1), pp. 720–725.
Hassan, A. S., Assar, S., Yahya, M., (2014). Estimation of R= P [Y< X] for Burr type XII distribution based on ranked set sampling. International Journal of Basic and Applied Sciences, 3(3), pp. 274–280.
Hassan, A. S., Assar, S., Yahya, M., (2015). Estimation of P (Y< X) for Burr distribution under several modifications for ranked set sampling. Australian Journal of Basic and Applied Sciences, 9(1), pp. 124–140.
Hassan, A. S., Elbagouri, R., Onyango, R., Nagy, H. F., (2022). Estimating system reliability using neoteric and median RSS data for generalized exponential distribution. International Journal of Mathematics and Mathematical Sciences, 2608656, https://doi.org/10.1155/2022/2608656.
Koyuncu, N., Karagöz, D., (2018). New mean charts for bivariate asymmetric distributions using different ranked set sampling designs. Quality Technology & Quantitative Management, 15(5), pp. 602–621.
Mahdizadeh, M., Arghami, N. R., (2010). Efficiency of ranked set sampling in entropy estimation and goodness-of-fit testing for the inverse Gaussian law. Journal of Statistical Computation and Simulation, 80(7), pp. 761–774.
Mcintyre, G., (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3(4), pp. 385–390.
Nadarajah, S., (2011). The exponentiated exponential distribution: a survey. AStA Advances in Statistical Analysis, 95, pp. 219–251.
Raqab, M. M., Ahsanullah, M., (2001). Estimation of the location and scale parameters of generalized exponential distribution based on order statistics. Journal of Statistical Computation and Simulation, 69(2), pp. 109–123.
Ristić, M. M., Balakrishnan, N., (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82(8), pp. 1191– 1206.
Sabry, M. A., Shaaban, M., (2020). Dependent ranked set sampling designs for parametric estimation with applications. Annals of Data Science, 7(2), pp. 357–371, https://doi.org/10.1007/s40745-020-00247-3.
Samawi, H. M., Ahmed, M. S., Abu-Dayyeh, W., (1996). Estimating the population mean using extreme ranked set sampling. Biometrical Journal, 38(5), pp. 577–586.
Samuh, M. H., Qtait, A., (2015). Estimation for the parameters of the exponentiated exponential distribution using a median ranked set sampling. Journal of Modern Applied Statistical Methods, 14(1), pp. 215–237.
Tahmasebi, S., Hosseini, E. H., Jafari, A. A., (2017). Bayesian estimation for Rayleigh distribution based on ranked set sampling. New Trends in Mathematical Sciences, 5(4), pp. 97–106.
Wolfe, D. A., (2010). Ranked set sampling. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4), pp. 460–466.
Zamanzade, E., Al-Omari, A. I., (2016). New ranked set sampling for estimating the population mean and variance. Hacettepe Journal of Mathematics and Statistics, 45(6), pp. 1891–1905.