Numerical computations indicate that certain of these estimators substantially improve the usual and minimum mean squared error (MMSE) estimators for value of the parameter near the prior estimate, especially for small sample sizes
📌 3 Maddede Bu Makale
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Amaç & Hipotez:This article proposes a class of shrinkage estimators of Morgenstern type bivariate exponential distribution (MTBED) based on concomitants of order statistic in ranked set sampling (RSS).
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Temel Bulgular & Veri:The class of estimators for the parameter is motivated by the work of Jani (1991).
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Sonuç & Katkı:Numerical computations indicate that certain of these estimators substantially improve the usual and minimum mean squared error (MMSE) estimators for value of the parameter near the prior estimate, especially for small sample sizes
🔬Tür:Araştırma Makalesi
📍Kapsam:2008 Verileri
⚙️Değişkenler:Ranked set sampling · Morgenstern type bivariate exponential distribution · Concomitants of order statistic
Abstract
This article proposes a class of shrinkage estimators of Morgenstern type bivariate exponential distribution (MTBED) based on concomitants of order statistic in ranked set sampling (RSS). The class of estimators for the parameter is motivated by the work of Jani (1991). The proposed class of shrinkage estimators has smaller mean square error (MSE) than the Chacko and Thomas (2008) estimators and minimum mean squared error (MMSE) estimators for wider range of the parameter. Numerical computations indicate that certain of these estimators substantially improve the usual and minimum mean squared error (MMSE) estimators for value of the parameter near the prior estimate, especially for small sample sizes
Mehta, V., Singh, H. P. (2022). Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 2, 575–591. https://ajindex.com/articles/530077
Al-Saleh, M. F. Steady-state ranked set sampling and parametric inference. Journal of Statistical Planning and Inference, 123, 83-95, (2004).
Al-Saleh, M. F. and Al-Kadiri, M. (2000).Double ranked set sampling. Statistics and Probability Letters, 48, 205-212.
Al-Saleh, M. F. and Al-Omari, A. (2002).Multistage ranked set sampling. Journal of Statistical Planning and Inference, 102, 273-286.
Barnett, V. and Moore, K. (1997).Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering. Journal of Applied Statistics, 24, 697-710.
Chacko, M. and Thomas, P. Y. (2008). Estimation of parameter of Morgenstern type bivariate exponential distribution by ranked set sampling. Annals of the Institute of Statistical Mathematics, 60,301-318.
Chen, Z. (2000).The efficiency of ranked-set sampling relative to simple random sampling under multi-parameter families. Statistica Sinica, 10, 247-263.
Chen, Z. and Bai, Z. (2000). The optimal ranked set sampling scheme for parametric families. Sankhya Series A, 46, 178-192.
Chen, Z., Bai, Z. and Sinha, B. K. (2004). Lecture notes in statistics, ranked set sampling, theory and applications. New York: Springer. Jani, P. N. (1991). A class of shrinkage estimators for the scale parameter of the exponential distribution. IEEE Transactions on Reliability, 40, 68-70.
Kourouklis, S. (1994). Estimation in the two-parameter exponential distribution with prior information. IEEE Transactions of Reliability, 43, 3446-450.
Lam, K., Sinha, B. K. and Wu, Z. (1994).Estimation of a two-parameter exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, 723-736.
Lam, K., Sinha, B. K. and Wu, Z. (1995). Estimation of location and scale parameters of a logistic distribution using ranked set sample. In: H. N. Nagaraja, P. K. Sen D. F. Morrison (Eds) Statistical theory and applications: papers in honor of Herbert A. David. New-York: Springer. McIntyre, G. A. (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3, 385-390.
Modarres, R. and Zheng, G. (2004). Maximum likelihood estimation of dependence parameter using ranked set sampling. Statistics and Probability Letters, 68, 315-323.
Scaria, J. and Nair, N. U. (1999). On concomitants of order statistics from Morgenstern family. Biometrical Journal, 41, 483-489.
Searls, D. T. and Intarapanich, P. (1990). A note on the estimator for the variance that utilizes