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Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling

Year 2016, Volume: 45 Issue: 2, 575 - 591, 01.04.2016

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

References

  • 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 the kurtosis. The American Statistician, 44, 295-296.
  • Searls, D.T. (1964). The utilization of a know coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 1225-1226.
  • Singh, J., Pandey, B. N. and Hirano, K. (1973). On the utilization of known coefficient of kurtosis in the estimation procedure of variance. Annals of the Institute of Statistical Mathematics, 25, 51-55.
  • Stokes, S. L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods, 6, 1207-1211.
  • Stokes, S. L. (1980). Inference on the correlation coefficient in bivariate normal populations from ranked set samples. Journal of the American Statistical Association, 75, 989-995.
  • Stokes, S. L. (1995). Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 47, 465-482.
  • Zheng, G. and Modarres, R. (2006). A robust estimate of correlation coefficient for bivariate normal distribution using ranked set sampling. Journal of Statistical planning and Inference, 136, 298-309.
Year 2016, Volume: 45 Issue: 2, 575 - 591, 01.04.2016

Abstract

References

  • 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 the kurtosis. The American Statistician, 44, 295-296.
  • Searls, D.T. (1964). The utilization of a know coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 1225-1226.
  • Singh, J., Pandey, B. N. and Hirano, K. (1973). On the utilization of known coefficient of kurtosis in the estimation procedure of variance. Annals of the Institute of Statistical Mathematics, 25, 51-55.
  • Stokes, S. L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods, 6, 1207-1211.
  • Stokes, S. L. (1980). Inference on the correlation coefficient in bivariate normal populations from ranked set samples. Journal of the American Statistical Association, 75, 989-995.
  • Stokes, S. L. (1995). Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 47, 465-482.
  • Zheng, G. and Modarres, R. (2006). A robust estimate of correlation coefficient for bivariate normal distribution using ranked set sampling. Journal of Statistical planning and Inference, 136, 298-309.
There are 22 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Housila P. Singh This is me

Vishal Mehta This is me

Publication Date April 1, 2016
Published in Issue Year 2016 Volume: 45 Issue: 2

Cite

APA P. Singh, H., & Mehta, V. (2016). Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 45(2), 575-591.
AMA P. Singh H, Mehta V. Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling. Hacettepe Journal of Mathematics and Statistics. April 2016;45(2):575-591.
Chicago P. Singh, Housila, and Vishal Mehta. “Some Classes of Shrinkage Estimators in the Morgenstern Type Bivariate Exponential Distribution Using Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 45, no. 2 (April 2016): 575-91.
EndNote P. Singh H, Mehta V (April 1, 2016) Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling. Hacettepe Journal of Mathematics and Statistics 45 2 575–591.
IEEE H. P. Singh and V. Mehta, “Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, pp. 575–591, 2016.
ISNAD P. Singh, Housila - Mehta, Vishal. “Some Classes of Shrinkage Estimators in the Morgenstern Type Bivariate Exponential Distribution Using Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 45/2 (April 2016), 575-591.
JAMA P. Singh H, Mehta V. Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2016;45:575–591.
MLA P. Singh, Housila and Vishal Mehta. “Some Classes of Shrinkage Estimators in the Morgenstern Type Bivariate Exponential Distribution Using Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, 2016, pp. 575-91.
Vancouver P. Singh H, Mehta V. Some classes of shrinkage estimators in the morgenstern type bivariate exponential distribution using ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2016;45(2):575-91.