Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A maximum likelihood estimation method for a mixture of shifted binomial distributions

  • Received : 2013.12.16
  • Accepted : 2014.01.13
  • Published : 2014.01.31
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Abstract

Many studies have estimated a mixture of binomial distributions. This paper considers an extension, a mixture of shifted binomial distributions, and the estimation of the distribution. The range of each component binomial distribution is rst evaluated and then for each possible value of shifted parameters, the EM algorithm is employed to estimate those parameters. From a set of possible value of shifted parameters and corresponding estimated parameters of the distribution, the likelihood of given data is determined. The simulation results verify the performance of the proposed method.

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References

  1. Blischke, W. (1964). Estimating the parameters of mixture of binomial distributions, Journal of the American Statistical Association, 59, 510-528. https://doi.org/10.1080/01621459.1964.10482176
  2. Bonnini, S., Piccolo, D., Salmaso, L. and Solmi, F. (2012). Permutation inference for a class of mixture models. Communications in Statistics-Theory and Methods, 41, 2879-2895. https://doi.org/10.1080/03610926.2011.590915
  3. Cekanavicius, V., Pekoz, E. A., Rollin, A. and Shwartz, M. (2009). A three- parameter binomial approximation. Avalable from http://arxiv.org/abs/0906.2855. https://doi.org/10.1239/jap/1261670689
  4. Copsey, K. and Webb, A. (2003). Bayesian gamma mixture model approach to radar target recognition. IEEE Transactions on Aerospace and Electronic Systems, 39, 1201-1217. https://doi.org/10.1109/TAES.2003.1261122
  5. Dempster, A. P., Laird, N. M. and Rubin, D. R. (1977). Maximum likelihood from incomplete data. Journal of the Royal Statistical Society B, 39, 1-38.
  6. Domenico, P. (2003). On the moments of a mixture of uniform and shifted binomial random variables. Quaderni di Statistica, 5, 1-20.
  7. Johnson, N. L., Kemp, A. W. and Kotz, S. (2005). Univariate discrete distributions, 3rd Ed., Wiley-Interscience, New York.
  8. Lee, H. J. and Oh, C. (2006). Estimation in mixture of shifted Poisson distributions with known shift parameters. Journal of the Korean Data & Information Science Society, 17, 785-794.
  9. Liu, Z., Almhana, J., Choulakian, V. and McGorman, R. (2006). Online EM algorithm for mixture with application to internet traffic modeling. Computational Statistics & Data Analysis, 50, 1052-1071. https://doi.org/10.1016/j.csda.2004.11.002
  10. McLachlan, G. J. and Krishnan, T. (2008). The EM algorithm and extensions, 2nd ed., Wiley, Hoboken, NJ.
  11. McLachlan, G. J. and Peel, D. (2001). Finite mixture models, John Wiley & Sons, Inc., New York.
  12. Oh, C. (2006). Estimation in mixture of shifted Poisson distributions. Journal of the Korean Data & Information Science Society, 17, 1209-1217.
  13. Park, C. (2013). Simple principle component analysis using Lasso. Journal of the Korean Data & Information Science Society, 24, 533-541. https://doi.org/10.7465/jkdi.2013.24.3.533
  14. Skipper, M. (2012). A Polya approximation to the Poisson-binomial law. Journal of Apply Probability, 49, 745-757. https://doi.org/10.1239/jap/1346955331
  15. Wasilewski, M. J. (1988). Estimation of the parametes of the mixture k>2 log- normal distributions. Trabajos de estadistica, 3, 167-175, https://doi.org/10.1007/BF02884332

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