Volume 9, Issue 4 Articles Tricks of the Trade In and Out Trott's Corner New Products New Publications Calendar News Bulletins New Resources Classifieds Download This Issue Editorial Policy Staff and Contributors Submissions Subscriptions Advertising Back Issues Contact Information 
MomentBased Density Approximants
References[1] H. Solomon and M. Stephens, "Approximations to Density Functions Using Pearson Curves," Journal of the American Statistical Association, 73(361), 1978 pp. 153160. [2] W. P. Elderton and N. L. Johnson, Systems of Frequency Curves, Oxford: Cambridge University Press, 1969. [3] C. Rose and M. D. Smith, Mathematical Statistics with Mathematica, New York: SpringerVerlag, 2002. [4] N. Reid, "Saddlepoint Methods and Statistical Inference," Statistical Science, 3(2), 1988 pp. 213238. [5] A. M. Mathai and R. K. Saxena, The Hfunction with Applications in Statistics and Other Disciplines, New York: John Wiley & Sons, 1978. [6] S. B. Provost and E. M. Rudiuk, "Moments and Densities of Test Statistics for Covariance Structures," International Journal of Mathematical and Statistical Sciences, 4(1), 1995 pp. 85104. [7] P. J. Smith, "A Recursive Formulation of the Old Problem of Obtaining Moments from Cumulants and Vice Versa," The American Statistician, 49, 1995 pp. 217219. [8] S. B. Provost and Y.H. Cheong, "On the Distribution of Linear Combinations of the Components of a Dirichlet Random Vector," The Canadian Journal of Statistics, 28, 2000 pp. 417425. [9] G. Sansone, Orthogonal Functions, Pure and Applied Mathematics, Vol. 9, New York: Interscience Publishers, 1959. [10] G. Alexits, Convergence Problems of Orthogonal Series, New York: Pergamon Press, 1961. [11] L. Devroye and L. Györfi, Nonparametric Density Estimation: The View, New York: John Wiley & Sons, 1985. [12] W. B. Jones and A. S. Ranga, eds., Orthogonal Functions, Moment Theory, and Continued Fractions, Theory and Applications, Lecture Notes in Pure and Applied Mathematics, New York: Marcel Dekker, 1998. [13] L. Devroye, "On Random Variate Generation When Only Moments or Fourier Coefficients Are Known," Mathematics and Computers in Simulation, 31, 1989 pp. 7189. [14] R. L. Burden and J. D. Faires, Numerical Analysis, 4th ed., Boston: PWSKent, 1989. [15] C. R. Rao, Linear Statistical Inference and Its Applications, New York: John Wiley & Sons, 1965. [16] A. M. Mathai, An Introduction to Geometric Probability: Distributional Aspects with Applications, The Netherlands: Gordon and Breach, 1999. [17] G. Szegö, Orthogonal Polynomials, Providence, RI: American Mathematical Society, 1959. [18] A. M. Mathai and S. B. Provost, Quadratic Forms in Random Variables, Theory and Applications, New York: Marcel Dekker, 1992. [19] J. T. Reinking, "Orthogonal Series Representations of Probability Density and Distribution Functions," The Mathematica Journal, 8(3), 2003 pp. 473483. [20] J. Gurland, "Distribution of Definite and of Indefinite Quadratic Forms," The Annals of Mathematical Statistics, 26, 1955 pp. 122127. [21] M. L. Tiku, "Laguerre Series Forms of Noncentral and Distributions," Biometrika, 52(3), 1965 pp. 415427. [22] N. L. Johnson and S. Kotz, Distributions in Statistics: Continuous Univariate Distributions, Vol. 2, New York: Wiley, 1970. [23] J. Durbin and G. S. Watson, "Testing for Serial Correlation in LeastSquares Regression II," Biometrika, 38(12), 1951 pp. 159178. [24] T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd ed., New York: John Wiley & Sons, 2003. [25] A. M. Mathai, "On the Distribution of the Likelihood Ratio Criterion for Testing Linear Hypotheses on Regression Coefficients," Annals of the Institute of Statistical Mathematics, 23, 1971 pp. 181197. [26] H. Cramér, "On Some Classes of Series Used in Mathematical Statistics," Proceedings of the Sixth Scandinavian Congress of Mathematicians, Copenhagen, 1925 pp. 399425.


About Mathematica  Download Mathematica Player © Wolfram Media, Inc. All rights reserved. 