Main Article Content
In this paper, the derivation of the likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) for the estimation of the parameters of the power generalized Weibull distribution is considered. The developed likelihood function is then used for the estimation of the exponential Pareto distribution parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) designs. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different designs. The relative efficiency of the DRSS estimates with respect to other designs was found to be higher in case of the exponential Pareto distribution (EP).
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Abed Al-Kadim K., Boshi M. A. (2013). "Exponential Pareto Distribution". Mathematical Theory and Modeling, 3(5): 135-146
Abu-Dayyeh, W. and Sawi, E. A. (2009). Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling. Statistical Papers, 50(2), 249-259.
Abu-Dayyeh, W., Assrhani, A., and Ibrahim, K. (2013). Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling. Statistical Papers, 54(1), 207-225.
Al-Odat, M. T., and Al-Saleh, M. F. (2001). A variation of ranked set sampling. Journal of Applied Statistical Science, 10(2), 137-146.
Al-Odat, N. A. (2009). Modiflcation in Ratio Estimator Using Rank Set Sampling. European Journal of Scientific Research ,volume 29, 265-268.
Al-Omari, A. and Al-Hadhrami, S. A. (2011). On maximum likelihood estimators of the parameters of a modified Weibull distribution using extreme ranked set sampling. Journal of Modern Applied Statistical Methods, 10(2), 607-617
Al-Omari, A. I., (2010). Improvement in Estimating the Population Mean in Double Extreme Ranked Set Sampling. International Mathematical Forum, 26:1265 – 1275.
Al-Omari, A. I., Al-Zubi , L. M. and Khazaleh, A. (2015). On the population median estimation using quartile double ranked set sampling. Pak.j.stat.oper.res., Vol. XI No.4 2015 pp513-524.
Al-Omari, Amer Ibrahim and Al-Hadhrami, Said Ali (2011) "On Maximum Likelihood Estimators of the Parameters of a Modified Weibull Distribution Using Extreme Ranked Set Sampling," Journal of Modern Applied Statistical Methods: Vol. 10 : Iss. 2 , Article 18.
Al-Saleh M.F., Al-Omari AI. (2002). Multistage ranked set sampling. Journal of Statistical Planning and Inference 102: 273–286
Al-Saleh, M.F. and Al-Hadrami, S.A. (2003). Estimation of the mean of the exponential distribution using moving extremes ranked set sampling. Statistical Papers 44, 367-382.
Al-Saleh, M.F. and Al-Hadrami, S.A. (2011). On maximum likelihood estimators of the parameters of a modified weibull distribution. Journal of Modern Applied Statistical Method, Volume 10 , Issue 2, 607-617.
Al-Saleh, M.F. and Al-Kadri, M.A. (2000). Double ranked set sampling. Statistics and Probability Letters 48, 205-212
Al-Saleh, M.F. and Zheng, G. (2002). Modified maximum likelihood estimator based on ranked set sampling. Annals of the Institute of Statistical Mathematics 54, 641–658.
Barry C. A., Balakrishnan N., Nagaraja, H. N., (2008)." A first course in Order Statistics". Classics in Applied Mathematics, Siam, Society for Industrial and Applied Mathematics- Philadelphia
Brar, S. S., Malik ,S. C. and Kaur ,J. (2017). Estimation of Median and Mode Using Ranked Set Sampling. International Journal of Statistics and Systems. ISSN 0973-2675, Volume 12, 525–533.
David H. A., Nagaraja H. N., (2005). "Order Statistics". Wiley Series in Probability and Statistics, John Wiley & Sons, Inc.
Dell, T.R. and Clutter, J. L. (1972). Ranked set sampling with order statistics background. Biometrics, 28, 545-553.
Essam M., Tang T. B., Wei Ho E. T., Chen H., (2017). "Dynamic Point Stochastic Rounding Algorithm for Limited Precision Arithmetic in Deep Belief Network Training". 8th International IEEE EMBS Conference on Neural Engineering, 629-632.
Halls, L.K. and Dell. T.R. (1966). Trials of ranked set sampling for forage yields. Forest Science, 12, 22-26.
Haq,A., Brown, J., Moltchanova, E., and Al-Omari, AI. (2013). Partial ranked set sampling design. wileyonlinelibrary.com DOI: 10.1002/env.2203
Hassan, A. S. (2013). Maximum likelihood and Bayes estimators of the unknown parameters for exponential distribution using ranked set sampling. International Journal of Engineering Research and Applications. 3, 720-725.
Höhfeld M., Fahlman S. E., (1992). "Probabilistic rounding in neural network learning with limited precision". Neurocomputing 4(6):291-299
Khamnei, H.J. and Mayan, S.R. (2016). Comparison of Parameter Estimation in the Exponentiated Gumbel Distribution based on Ranked Set Sampling and Simple Random Sampling. Journal of Mathematics and Statistical Science, Volume 2016, 490-497
Maharota, K. and Nanda, P. (1974). Unbiased estimator of parameter by order statistics in the case of censored samples. Biometrika, 61(3), 601-606.
McIntyre, G.A. (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3, 385-390.
Muttlak, H. A. (1997). `Median ranked set sampling', Journal of Applied Statistics Sciences, 6.
Muttlak, H.A. (2003). Modified ranked set sampling methods. Pakistan Journal of Statistics, 19, 315-323.
Samawi, H. M., Ahmed, M. S. and Abu-Dayyeh, W. A. (1996). Estimating the population mean using extreme ranked set sampling. The Biometrical J., 38(5), 577-586.
Weibull W. (1951). "A statistical distribution function of wide applicability". J Appl Mech;18:293-297.
Wolfe, D.A. 2004. Ranked set sampling: an approach to more efficient data collection. Statistical Science, 19(4): 636-643