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1: 1.16 Distributions
§1.16(i) Test Functions
The linear space of all test functions with the above definition of convergence is called a test function space. … … Tempered distributions are continuous linear functionals on this space of test functions. …
2: 4.48 Software
Links to research literature for the Lambert W -function and for test software are included also. …
3: 23.20 Mathematical Applications
§23.20(iii) Factorization
4: 35.9 Applications
For other statistical applications of F q p 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). …
5: Software Index
  • Commercial Software.

    Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

  • 6: Bibliography G
  • P. Groeneboom and D. R. Truax (2000) A monotonicity property of the power function of multivariate tests. Indag. Math. (N.S.) 11 (2), pp. 209–218.
  • 7: Daniel W. Lozier
    His research interests have centered on numerical analysis, special functions, computer arithmetic, and mathematical software construction and testing. …
    8: Errata
  • Subsection 1.16(vii)

    Several changes have been made to

    1. (i)

      make consistent use of the Fourier transform notations ( f ) , ( ϕ ) and ( u ) where f is a function of one real variable, ϕ is a test function of n variables associated with tempered distributions, and u is a tempered distribution (see (1.14.1), (1.16.29) and (1.16.35));

    2. (ii)

      introduce the partial differential operator D in (1.16.30);

    3. (iii)

      clarify the definition (1.16.32) of the partial differential operator P ( D ) ; and

    4. (iv)

      clarify the use of P ( D ) and P ( x ) in (1.16.33), (1.16.34), (1.16.36) and (1.16.37).

  • 9: Bibliography C
  • W. J. Cody (1993a) Algorithm 714: CELEFUNT – A portable test package for complex elementary functions. ACM Trans. Math. Software 19 (1), pp. 1–21.
  • W. J. Cody (1993b) Algorithm 715: SPECFUN – A portable FORTRAN package of special function routines and test drivers. ACM Trans. Math. Software 19 (1), pp. 22–32.
  • 10: Bibliography B
  • D. K. Bhaumik and S. K. Sarkar (2002) On the power function of the likelihood ratio test for MANOVA. J. Multivariate Anal. 82 (2), pp. 416–421.