Estimation of Gini Index of the Exponential Distribution by Bootstrap Method

  • Kang, Suk-Bok (Department of Statistics, Yeungnam University, Kyongsan 712, 749) ;
  • Cho, Young-Suk (Department of Statistics, Yeungnam University, Kyongsan, 712-749)
  • Published : 1996.12.01

Abstract

In this paper, we propose the jackknife estimator and the bootstrap estimator of Gini index of the two-parameter exponential distribution when the location parameter $\theta$ is unknown and the scale parameter $\sigma$is known. Sinilarly, we propose the bias location parameter $\theta$ and the scale parameter $\sigma$ are unknown. The bootstrap estimator is more efficient than the other estimators when the location parameter $\theta$is unknown and the scale parameter $\sigma$ is known, and the bias corrected estimator is more efficient than the MLE when both the location parameter $\theta$ and the scale parameter $\sigma$are unknown.

Keywords

References

  1. Ann. Statist. v.7 Bootstrap Methods: Another Look at the Jackknife Efron, B.
  2. An Introduction to the Bootstrap Efron, B;Tishirani, R. J.
  3. Table of Integrals, Series, and Products Grodshteyn, I. S;Ryzhik, I. M.
  4. Biometrika v.61 The Jacknife-a review Miller, R. G.
  5. Ann. Inst. Statist. Math. v.37 Distribution of Maximum Likelihood Estimators of Lorenz Curve and Gini Index of Exponential Distribution Moothathu, T. S. K.
  6. Sankhya(series B) v.47 Sampling Distribution of Lorenz Curve and Gini Index of the Pareto Distribution Moothathu, T. S. K.
  7. Sankhya(series B) v.52 The Best Estimator of Lorenz Curve, Gini Index and Theil Entropy Index of pareto Distribution Moothathu, T. S. K.
  8. Biometrika v.43 Notes on Bias in Estimation Quenouille, M.
  9. Ann. Math. Statist. v.29 Bias and Confidence in not Quite Large Samples(abstract) Tukey, J. W.`