Journal of the Korean Statistical Society

  • 제33권3호
  • /
  • Pages.323-337
  • /
  • 2004
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

ESTIMATING VARIOUS MEASURES IN NORMAL POPULATION THROUGH A SINGLE CLASS OF ESTIMATORS

  • Sharad Saxena (Institute of Management, Nirma University of Science & Technology) ;
  • Housila P. Singh (School of Studies in Statistics, Vikram University)
  • 발행 : 2004.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This article coined a general class of estimators for various measures in normal population when some' a priori' or guessed value of standard deviation a is available in addition to sample information. The class of estimators is primarily defined for a function of standard deviation. An unbiased estimator and the minimum mean squared error estimator are worked out and the suggested class of estimators is compared with these classical estimators. Numerical computations in terms of percent relative efficiency and absolute relative bias established the merits of the proposed class of estimators especially for small samples. Simulation study confirms the excellence of the proposed class of estimators. The beauty of this article lies in estimation of various measures like standard deviation, variance, Fisher information, precision of sample mean, process capability index $C_{p}$, fourth moment about mean, mean deviation about mean etc. as particular cases of the proposed class of estimators.

키워드

참고문헌

  1. JAMES, W. AND STEIN, C. (1961). 'Estimation with quadratic loss', Proceedings of the 4th Berkeley Symposium on Mathematical Statistics, I, University of California Press, Berkley, CA, 361-379
  2. MEHTA, J. S. AND SRINIVASAN, R. (1971). 'Estimation of the mean by shrinkage to a point', Journal of the American Statistical Association, 66, 86-90 https://doi.org/10.2307/2284853
  3. PANDEY, B. N. (1979). 'On shrinkage estimation of normal population variance', Communications in Statistics- Theory and Methods, 8, 359-365 https://doi.org/10.1080/03610927908827765
  4. PANDEY, B. N. AND SINGH, B. P. (1978). 'On estimation of rth power of scale in exponential distribution from complete and censored samples', Progress of Mathematics, 12, 51-57
  5. PANDEY, B. N. AND SINGH, J. (1977). 'Estimation of the variance of normal population using prior information', Journal of the Indian Statistical Association, 15, 141-150
  6. SAXENA, S. (2002). Improved Estimation of Parameter(s) Using Prior Information, Unpublished Ph. D. Thesis, Vikram University, Ujjain, MP, India
  7. SINGH, H. P. AND SAXENA, S. (2003). 'An improved class of shrinkage estimators for the variance of a normal population', Statistics in Transition, 6, 119-129
  8. SINGH, H. P. AND SHUKLA, S. K. (1999). 'Families of shrinkage estimators of kth power of scale parameters in exponential distribution from complete and censored samples', Journal of Statistical Studies, 19, 29-35
  9. SINGH, H. P., SHUKLA, S. K. AND KATYAR, N. P. (1999). 'Estimation of standard deviation in normal distribution with prior information', Proceedings of the National Academic Sciences India, 69, 183-189
  10. SINGH, H. P. AND SINGH, R. (1997). 'A class of shrinkage estimators for the variance of a normal population', Microelectronics & Reliability, 37, 863-867 https://doi.org/10.1016/S0026-2714(96)00103-5
  11. SINHA, S. K. AND KALE, B. K. (1980). Life Testing and Reliability Estimation, Wiley Eastern, New Delhi, India, 152
  12. THOMPSON, J. R. (1968). 'Some shrinkage techniques for estimating the mean', Journal of the American Statistical Association. 63. 113-122 https://doi.org/10.2307/2283832