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Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data

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  • Cesar Augusto Taconeli

    (Federal University of Paraná)

  • Suely Ruiz Giolo

    (Federal University of Paraná)

Abstract

Ranked set sampling (RSS) has been proved to be a cost-efficient alternative to simple random sampling (SRS). However, there are situations where some measurements are censored, which may not ensure the superiority of RSS over SRS. In this paper, the performance of the maximum likelihood estimators is examined when the data are assumed to follow a Power Lindley or a Weighted Lindley distribution, and are collected according to the original RSS or one of its two variations (the median and extreme RSS). An extensive simulation study, considering uncensored and right-censored data, and perfect and imperfect ranking, is carried out based on the two mentioned distributions in order to compare the performance of the maximum likelihood estimators from RSS-based designs with the corresponding SRS estimators. Two illustrations are presented based on real data sets. The first involves the lifetimes of aluminum specimens, while the second deals with the amount of spray mixture deposited on the leaves of apple trees.

Suggested Citation

  • Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00984-2
    DOI: 10.1007/s00180-020-00984-2
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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Frey, Jesse & Ozturk, Omer & Deshpande, Jayant V., 2007. "Nonparametric Tests for Perfect Judgment Rankings," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 708-717, June.
    3. Saeid Amiri & Reza Modarres & Silvelyn Zwanzig, 2017. "Tests of perfect judgment ranking using pseudo-samples," Computational Statistics, Springer, vol. 32(4), pages 1309-1322, December.
    4. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    5. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    6. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    7. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    8. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    9. Walid Abu-Dayyeh & Aissa Assrhani & Kamarulzaman Ibrahim, 2013. "Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling," Statistical Papers, Springer, vol. 54(1), pages 207-225, February.
    10. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    11. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    12. M. Mahdizadeh & E. Strzalkowska-Kominiak, 2017. "Resampling based inference for a distribution function using censored ranked set samples," Computational Statistics, Springer, vol. 32(4), pages 1285-1308, December.
    13. Gang Zheng & Mohammad Al-Saleh, 2002. "Modified Maximum Likelihood Estimators Based on Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 641-658, September.
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    Cited by:

    1. Rajni Goel & Hare Krishna, 2022. "Statistical inference for two Lindley populations under balanced joint progressive type-II censoring scheme," Computational Statistics, Springer, vol. 37(1), pages 263-286, March.
    2. Yusuf Can Sevil & Tugba Ozkal Yildiz, 2022. "Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling," Computational Statistics, Springer, vol. 37(4), pages 1695-1726, September.

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