tempered%20distributions
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21: 35.9 Applications
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►In multivariate statistical analysis based on the multivariate normal distribution, the probability density functions of many random matrices are expressible in terms of generalized hypergeometric functions of matrix argument , with and .
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►For other statistical applications of functions of matrix argument see Perlman and Olkin (1980), Groeneboom and Truax (2000), Bhaumik and Sarkar (2002), Richards (2004) (monotonicity of power functions of multivariate statistical test criteria), Bingham et al. (1992) (Procrustes analysis), and Phillips (1986) (exact distributions of statistical test criteria).
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►In the nascent area of applications of zonal polynomials to the limiting probability distributions of symmetric random matrices, one of the most comprehensive accounts is Rains (1998).
22: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
23: 23 Weierstrass Elliptic and Modular
Functions
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24: 1.11 Zeros of Polynomials
25: Bibliography P
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Handbook of the Normal Distribution.
Statistics: Textbooks and Monographs, Vol. 40, Marcel Dekker Inc., New York.
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The exact distribution of the Wald statistic.
Econometrica 54 (4), pp. 881–895.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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26: 1.1 Special Notation
27: Ingram Olkin
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►Olkin’s research covered a broad range of areas, including multivariate analysis, reliability theory, matrix theory, statistical models in the social and behavioral sciences, life distributions, and meta-analysis.
… Hedges), published by Academic Press in 1985, and Life
Distributions: Non-Parametric, Semi-Parametric, and Parametric Families (with A.
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28: 1.14 Integral Transforms
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1.14.1
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►The same notation is used for Fourier transforms of functions of several variables and for Fourier transforms of distributions; see §1.16(vii).
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29: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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The computation of lattice frequency distribution functions by means of continued fractions.
Physica 39 (3), pp. 413–423.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Algorithm 322. F-distribution.
Comm. ACM 11 (2), pp. 116–117.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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30: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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On the distribution of the length of the longest increasing subsequence of random permutations.
J. Amer. Math. Soc. 12 (4), pp. 1119–1178.
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Moment equations for probability distributions in classical and quantum mechanics.
Phys. Rev. A 58 (3), pp. 1799–1809.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and Procrustes analysis.
J. Multivariate Anal. 41 (2), pp. 314–337.
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