Estimation of the Mean and Variance for Normal Distributions whose Both Sides are Truncated



Hong, Chong-Sun;Choi, Yun-Young

  • 발행 : 2002.04.01


In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.


Bias;Censored-sample estimators;Full-sample estimators;MSE


  1. Technometrics v.3 pp.433-438 Tables for Maximum Likelihood Estimation: Singly Truncated and Singly Censored Samples Cohen, A.
  2. Annals of the Mathematical Statistics v.21 pp.557-569 Estimating the Mean and Variance of Normal Populations from Singly Truncated and Doubly Truncated Samples Cohen, A.
  3. Journal of the American Statistical Association v.44 pp.518-525 On Estimating the Mean and Standard Deviation of Truncated Normal Distributions Cohen, A.
  4. Continuous Univariate Distribution-1 Johnson, N.;Kotz, S.
  5. Journal of the American Statistical Association v.47 pp.457-465 Estimation in the Truncated Nromal Distribution Halperin, M.
  6. Technometrics v.1 pp.217-237 Simplified Estimation for the Normal Distribution when Samples are Singly Censored or Truncated Cohen, A.
  7. Reliability Engineering Handbook v.1 Keceioglu, D.
  8. Biometrika v.39 pp.260-273 Estimation of the Mean and Standard Deviation of the Normal Population from a Censored Sample Gupta, A.
  9. Statistical Thoery with Engineering Applications Hald, A.
  10. British Association for the Advancement of Science v.5 The Truncated Nromal Distribution Fisher, R.
  11. The American Statistician v.53 no.4 pp.357-361 Mean and Variance of truncated Normal Distribution Barr, D.;Sherrill, E.
  12. Truncated and Censored Samples: Theory and Application Cohen, A.