Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Modified inverse moment estimation: its principle and applications

  • Gui, Wenhao (Department of Mathematics, Beijing Jiaotong University)
  • Received : 2016.10.30
  • Accepted : 2016.11.11
  • Published : 2016.11.30
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Abstract

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

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References

  1. Afify WM (2010). On estimation of the exponentiated Pareto distribution under different sample schemes, Statistical Methodology, 7, 77-83. https://doi.org/10.1016/j.stamet.2009.10.003
  2. Ahmadi J and Balakrishnan N (2009). Distribution-free confidence intervals for quantiles and tolerance intervals in terms of k-records, Journal of Statistical Computation & Simulation, 79, 1219-1233. https://doi.org/10.1080/00949650802232633
  3. Ali MM, Pal M, and Woo J (2010). On the ratio of two independent exponentiated Pareto variables, Austrian Journal of Statistics, 39, 329-340.
  4. Arnold BC, Balakrishnan N, and Nagaraja HN (1992). A First Course in Order Statistics, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104).
  5. Cheng TCF, Ing CK, and Yu SH (2014). Inverse moment bounds for sample autocovariance matrices based on detrended time series and their applications, Linear Algebra & Its Applications, 473, 180-201.
  6. Gu BQ and Yue RX (2013). Some notes on parameter estimation for generalized exponential distribution, Communication in Statistics - Theory and Methods, 42, 1787-1805. https://doi.org/10.1080/03610926.2011.597918
  7. Gui W (2015). Exponentiated half logistic distribution: different estimation methods and joint confidence regions, Communication in Statistics - Simulation and Computation, http://doi.org/10.1080/03610918.2015.1122053
  8. Gupta RC, Gupta PL, and Gupta RD (1998). Modeling failure time data by Lehman alternatives, Communication in Statistics - Theory and Methods, 27, 887-904. https://doi.org/10.1080/03610929808832134
  9. Raqab MZ (2013). Discriminating between the generalized Rayleigh and Weibull distributions, Journal of Applied Statistics, 40, 1480-1493. https://doi.org/10.1080/02664763.2013.788614
  10. Raqab MZ (2006). Nonparametric prediction intervals for the future rainfall records, Environmetrics, 17, 457-464. https://doi.org/10.1002/env.781
  11. Shawky AI and Abu-Zinadah HH (2009). Exponentiated Pareto distribution: different method of estimations, International Journal of Contemporary Mathematical Sciences, 4, 677-693.
  12. Singh SK, Singh U, Kumar M, and Singh GP (2013). Estimation of parameters of exponentiated Pareto distribution for progressive type-II censored data with binomial random removals scheme, Electronic Journal of Applied Statistical Analysis, 6, 130-148.
  13. Wang BX (1992). Statistical inference for Weibull distribution, Chinese Journal of Applied Probability & Statistics, 8, 357-364.
  14. Wang BX (2004). Statistical analysis for the Weibull distribution based on type II progressively censored data, Bulletin of Science & Technology, 6, 488-490.
  15. Wang X, Hu S, Yang W, and Ling N (2010). Exponential inequalities and inverse moment for NOD sequence, Statistics & Probability Letters, 80, 452-461. https://doi.org/10.1016/j.spl.2009.11.023
  16. YangW, Hu S, andWang X (2014). On the asymptotic approximation of inverse moment for nonnegative random variables, Communication in Statistics - Theory and Methods, http://doi.org/10.1080/03610926.2013.781648
  17. Ye Z and Yang J (2013). Sliced inverse moment regression using weighted chi-squared tests for dimension reduction, Journal of Statistical Planning & Inference, 140, 3121-3131.

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