New Parametric Estimation Methods based on Ranked Set Sampling

Year 2019, Volume: 32 Issue: 4, 1356 - 1368, 01.12.2019

Mohamed Abdallah Samir Ashour

https://doi.org/10.35378/gujs.477631

Cited By: 1

Abstract

The problem of parameters estimation plays a
significant role in various areas of academic researches. In this article, we
propose three different methods of estimation for the parameters of
location-scale family under ranked set sampling in the view of missing data
mechanism. Through a series of Monte Carlo simulations, it is well investigated
that the proposed methods are relatively robust from violating the perfect
ranking condition and provide better performance over their competitors using
bias and MSE (mean square error) criteria. An empirical data set is also used
for illustrative purposes.

Keywords

Cramér-von-Mises, EM algorithm, Estimation methods, Missing Data Approach, Ranked set sampling

References

• [1.] Abu-Dayyeh, W. Assrhani, A., Ibrahim, K. “Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling ”, Statistical Papers. 54: 207–225, (2013).‏[2.] Ashour, S. and Abdalluh, M. “New Distribution Function Estimation and Perfectness Testing under Ranked Set Sampling ”. To appear in Journal of Modern Applied Statistical Methods, (2018a).[3.] Ashour, S. and Abdalluh, M. “Estimation of Distribution Function based on Ranked Set Sampling: Missing Data Approach”. To appear in Thailand Statistician, (2018b).[4.] Cabana, A. and Quiroz, AJ. “Using the empirical moment generating function in testing for the Weibull and the type I extreme value distributions”. Test. 14(2): 417-431, (2005)[5.] Cheng, R. and Amin, N. “Estimating parameters in continuous univariate distributions with a shifted origin”. Journal of the Royal Statistical Society. Series B .45. 394 -403, (1983).[6.] Dell, TR. and Clutter, JL. “Ranked set sampling theory with order statistics background”. Biometrics 28(2): 545-555, (1972)[7.] Dey, S. Salehi, M. Ahmadi, J. “Rayleigh distribution revisited via ranked set sampling”. Metron. 75(1): 69-85, (2017).[8.] Frey, J. and Zhang, Y. “An algorithm with applications in ranked-set sampling”. Journal Statistical Computation Simulation; 88(3): 471-481, (2018).[9.] Frey, J. Ozturk, O. and Deshpande, J.V. “Nonparametric tests for perfect judgment rankings”. Journal of the American Statistical Association. 102(478): 708–717, (2007).[10.] Hassan, A. “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. 720-725, (2013).[11.] Macdonald, P. “An estimation procedure for mixtures of distribution”, Journal of the Royal Statistics Society, Series B (Methodological) 33: 326–329, (1971).[12.] Mahdizadeh, M. and Zamanzade, E. “A new reliability measure in ranked set sampling”. Statistical Paper. 59 (3): 861-891, (2018).[13.] Mahdizadeha, M. and Tamandi, M. “A new approach to parameter estimation in ranked set sampling”. International Journal of Statistics & Economics. 17(1): 40-49, (2016).[14.] McIntyre, GA. “A method for unbiased selective sampling using ranked set sampling”. Australian Journal of Agricultural Research. 3: 385-390, (1952).[15.] Mittelhammer, RC. “Mathematical Statistics for Economics and Business”. Springer Science + Business Media, (2013).[16.] Ozturk, O. “Statistical inference under a stochastic ordering constraint in ranked set sampling”. Nonparametric Statistics, 19: 131–144, (2007).[17.] Ozturk, O. “Parametric estimation of location and scale parameters in ranked set sampling”. Journal of Statistical Planning and Inference. 141(4): 1616-1622, (2011).‏[18.] Rajagopalan, M and Dhanavanthan, P. “Statistical inference”. PHI Learning Private Limited, (2012).[19.] Sarikavanij, S. Kasala, S., Sinha, B.K. and Tiensuwan, M. “Estimation of location and scale parameters in two-parameter exponential distribution based on ranked set sampling”. Communications in Statistics-Simulation and Computation 43(1): 132–141, (2014).[20.] Stokes, SL. “Parametric ranked set sampling”. Annals of the Institute of Statistical Mathematics. 47. 465–482, (1995).[21.] Wu, C. “On the Convergence Properties of the EM Algorithm”. The Annals of Statistics, 11(1): 95-103, (1983).[22.] Yousef, O. and Al-Subh, SA. “Estimation of Gumbel parameters under ranked set sampling”. Journal of Modern Applied Statistical Methods. 13(2): 432-443, (2014).[23.] Zamanzade, E. “EDF-based tests of exponentiality in pair ranked set sampling”. Statistical Papers, 1-19, (2018).[24.] Zamanzade, E. and Mahdizadeh, M. “Distribution function estimation using concomitant-based ranked set sampling”. Hacettepe Journal of Mathematics and Statistics. 47(3): 755-761, (2018).[25.] Zamanzade, E. and Mohammadi, M. “Some modified mean estimator in ranked set sampling using a covariate”. Journal of Statistical Theory and Applications. 15(2): 142-152, (2016).