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American Journal of Mathematical and Management Sciences Volume 9, 1989 - Issue 1-2: Distributions of Test Statistics: Exact & Asymptotic, Null & Non-Null, Methods/Comparisons/Research Frontiers
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Original Articles

Some Common Structures of Distribution Problems in Geometric Probabilities and Multivariate Statistical Analysis

A. M. MathaiMcGill University, Canada
&
G. PederzoliUniversity of Trento, Italy
Pages 113-139 | Published online: 14 Aug 2013

  • AndersonW. J. (1986). On certain random simplices in Rn. Journal of Multivariate Analysis, 19, 265–272.
  • JairuD. N. (1987). Distributions of Some Random Volumes and Their Connection to Multivariate Analysis. M. Sc. Thesis. McGill University.
  • MathaiA. M. (1979). The exact distribution and the exact percentage points for testing equality of variances in independent normal populations. Journal of Statistical Computation and Simulation, 9, 169–182.
  • MathaiA. M. (1982). On a conjecture in geometric probability regarding asymptotic normality of a random simplex. Annals of Probability, 10, 247–251.
  • MathaiA. M. (1983). Exact densities of the random r-contents of the beta distributed random points in an n-ball. Sankhyā Series A, 45, 313–323.
  • MathaiA. M. (1984). Extensions of Wilks' integral equations and distributions of test statistics. Annals of the Institute of Statistical Mathematics, 36, 271–288.
  • MathaiA. M. (1984a). On multisample sphericity (in Russian). Investigations in Statistics (Russian) Tom 136, 153–161, 1984.
  • MathaiA. M. (1985). Exact and asymptotic procedures in the distribution of multivariate test statistics. (Statistical Theory and Data Analysis, MatusitaK. Ed., North-Holland, 1985, 381–418.).
  • MathaiA. M. (1988). On a system of differential equations connected with the gravitational instability of a multicomponent medium in Newtonian cosmology. Studies in Applied Mathematics (1988, to appear).
  • MathaiA. M. and Katiyar (1979). Exact percentage points for testing independence. Biometrika, 66, 353–356.
  • MathaiA. M. and KatiyarR. S. (1979a). The distribution and the exact percentage points for Wilks' Lmvc criterion. Annals of the Institute of Statistical Mathematics, 31, 215–224.
  • MathaiA. M. and KatiyarR. S. (1980). Exact percentage points for three tests associated with exponential populations. Sankhyā Series B, 42, 33–41.
  • MathaiA. M. and PederzoliG. (1985). A direct statistical technique of obtaining some summation formulae for Bernoulli polynomials. Metron XLIII N. 3–4, 157–166.
  • MathaiA. M. and RathieP. N. (1980). Exact non-null distribution for testing equality of covariance matrices. Sankhyā Series A, 42, 78–87.
  • MathaiA. M. and SaxenaR. K. (1973). Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences. Springer–Verlag (Lecture Notes No. 348), Heidelberg and New York.
  • MathaiA. M. and SaxenaR. K. (1978). The H- Function With Applications in Statistics and Other Disciplines. Wiley, Halsted, New York.
  • MathaiA. M. and TracyD. S. (1983). On a random convex hull in an n-ball. Communciations in Statistics. Theory and Methods. 12 (15), 1727–1736.
  • PederzoliG. (1985). On uniformly distributed random points in an n-ball. Communications in Statistics. Theory and Methods, 14 (1), 185–194.
  • PederzoliG. (1985a). On beta type-I distributed random points in an n-ball. Communciations in Statistics. Theory and Methods, 14(1), 195–202.
  • PederzoliG. (1986). A representation in beta series for the exact density of some random volume contents. Communications in Statistics. Theory and Methods, A15 (11), 3299–3306.
  • PederzoliG. (1986a). Computable representations for general density of random r-contents of beta distributed random points in an n-ball. Statistica, 17 (3), 445–451.
  • PederzoliG. (1986b). Exact densities associated with uniformly distributed random points in an n-ball. South African Statistical Journal, 20 (1), 19–28.
  • PederzoliG. (1987). Mixture representations of the random volume content of beta distributed random points in an n-ball. Sankhyā Series A, 49, 43–49.
  • MilesR. E. (1971). Isotropic random simplices. Advances in Applied Probability, 3, 353–382.
  • RubenH. (1977). The volume of a random simplex in an n-ball is asymptotically normal. Journal of Applied Probability, 14, 647–653.
  • RubenH. (1980). A canonical decomposition of the probability measure of sets of isotropic random points in Rn. Journal of Multivariate Analysis, 10, 1–18.

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