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Original Articles

Nonlinear Discriminant Functions for Mixed Random Walk Models

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Pages 1923-1938 | Received 13 Mar 2010, Accepted 01 Sep 2010, Published online: 19 Nov 2010

References

  • Abdel-All , N. H. , Abd Ellah , H. N. , Moustafa , H. M. ( 2003 ). Information geometry of random walk distribution . Publ. Math. Debrecen 63/1–2 : 51 – 66 .
  • Ahmad , K. E. ( 1987 ). Generating random vectors from a bivariate random walk density function . J. Statistical. Computation and Simulation 27 : 243 – 250 .
  • Ahmad , K. E. ( 1993 ). Rrandom walk density function with unknown origin . Math. Comput. Modelling 18 ( 8 ): 83 – 92 .
  • Ahmad , K. E. ( 1994 ). Small sample results for a nonlinear discriminant function estimated from a mixture of two Burr type XII distributions . Computers and Mathematics with Applications 28 : 13 – 20 .
  • Ahmad , K. E. ( 1995 ). The efficiency of a nonlinear discriminant function based on unclassified initial samples from a mixture of two Burr type XII populations . Computers and Mathematics with Applications 30 : 1 – 7 .
  • Amoh , R. K. ( 1985 ). Estimation of a discriminant function from a mixture of two inverse Gaussian distributions when the sample size is small . Journal of Statistical Computation Simulation 20 : 275 – 286 .
  • Broyden , C. G. ( 1965 ). A class of methods for solving nonlinear simultaneous equations . Mathmatics of Computation 19 : 577 – 593 .
  • Burden , R. L. , Faires , J. D. (1985). Numerical Analysis. , 3rd ed.Boston : Prindle, Weber & Schmidt.
  • Choi , K. ( 1969 ). Estimates for the parameters of a finite mixture distributions . Annerican. Institute of Statistical. Mathematics 21 : 107 – 116 .
  • Dempster , A. P. , Laird , N. M. , Rubin , D. B. ( 1977 ). Maximum likelihood from incomplete data via the EM algorithm . Journal of Royal Statistical Society B 39 : 1 – 38 .
  • EL Hussaini , E. K. , Ahmad , K. E. ( 1981 ). On the identifiability of finite mixtures of distributions . IEEE Transaction Information Theory IT 27 ( 5 ): 664 – 668 .
  • Fukunga , K. , Kassell , D. ( 1973 ). Non parametric Bayes error estimation using unclassified samples . IEEE Saction Information Theory IT 19 : 434 – 440 .
  • Ganasalingam , S. , Mclachlan , G. J. ( 1978 ). The efficiency of a linear discriminant function based on unclassified initial samples . Biometrika 65 : 658 – 662 .
  • Ganasalingam , S. , Mclachlan , G. J. ( 1979 ). Small sample results for a linear discriminant function estimated from a mixture of normal populations . Journal of Statistical Computation and Simulation 9 : 151 – 158 .
  • IMSL. ( 1984 ). Reference Manual , Fortran Library, Inc. Houston , TX .
  • Jaheen , Z. F. ( 1999 ). Bayesian estimation for the three parameters of the random walk distribution . Journal of Applied Statistical Science 8 ( 2/3 ): 187 – 195 .
  • Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1994 ). Continuous Univariate Distributions . Vol. 1 . , 2nd ed. New York : John Wiley & Sons. Inc .
  • Mahmoud , M. A. W. , Moustafa , H. M. ( 1993 ). Estimation of a discriminant function from a mixture of two Gamma distributions when the sample size is small . Mathematical and Computer Modelling 18 : 87 – 95 .
  • Mahmoud , M. A. W. , Moustafa , H. M. ( 1995 ). Errors of misclassification associated with Gamma distribution . Mathematical and Computer Modeling 22 : 105 – 119 .
  • Moore , D. S. , Whitsitt , S. J. , Landgrebe , D. A. ( 1976 ). Variance comparisons for unbiased estimators of probability of correct classification . IEEE Transaction of Information Theory IT 22 : 102 – 105 .
  • Moustafa , H. M. , Ramadan , S. J. ( 2003 ). On MLE of a nonlinear discriminant function from a mixture of two Gompertz distributions based on small sample size . Journal of Statistical Computation and Simulations 00 : 1 – 19 .
  • O'Neill , T. J. ( 1978 ). Normal discriminant with unclassified observations . Journal of the American Statistical Association 73 : 821 – 826 .
  • Ross , S. M. ( 1996 ). Stochastic Processes. , 2nd ed. New York : John Wiley & Sons. Inc .
  • Rubinstein , R.Y. ( 1981 ). Simulation and the Monte Carlo Method . New York : John Wiley & Sons. Inc .
  • Tweedie , M. C. K. ( 1956 ). Some statistical properties of the inverse Gaussian distribution . Virginia Journal of science 7 : 160 – 165 .
  • Wasan , M. T. ( 1969 ). First passage time distribution of Brownian motion . Monograph, Dept. Mathematics. Kingston , Ontario , Canada : Queen's University .
  • Wise , M. E. ( 1966 ). Tracer dilution curves in cardiology and random walk and lognormal distribution . Acta Physiologic Pharamacologica Nederlandica 14 : 175 – 204 .

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