probability distribution

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1: 24.18 Physical Applications

… ►Bernoulli polynomials appear in statistical physics (Ordóñez and Driebe (1996)), in discussions of Casimir forces (Li et al. (1991)), and in a study of quark-gluon plasma (Meisinger et al. (2002)). ►Euler polynomials also appear in statistical physics as well as in semi-classical approximations to quantum probability distributions (Ballentine and McRae (1998)).

2: 19.31 Probability Distributions

§19.31 Probability Distributions

► $R_G(x,y,z)$ and $R_F(x,y,z)$ occur as the expectation values, relative to a normal probability distribution in ${ℝ}^2$ or ${ℝ}^3$, of the square root or reciprocal square root of a quadratic form. …

3: 35.9 Applications

… ►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 ${}_p{}^{}F_q^{}$, with $p\le 2$ and $q\le 1$. … ►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).

4: Bibliography B

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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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§24.18.

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5: 8.23 Statistical Applications

… ►The functions $P(a,x)$ and $Q(a,x)$ are used extensively in statistics as the probability integrals of the gamma distribution; see Johnson et al. (1994, pp. 337–414). …

6: 3.5 Quadrature

… ►In more advanced methods points are sampled from a probability distribution, so that they are concentrated in regions that make the largest contribution to the integral. …

7: 7.20 Mathematical Applications

… ►For applications in statistics and probability theory, also for the role of the normal distribution functions (the error functions and probability integrals) in the asymptotics of arbitrary probability density functions, see Johnson et al. (1994, Chapter 13) and Patel and Read (1982, Chapters 2 and 3).

8: Bibliography H

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Computation of certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven 1968 (2), pp. 81–104. (errata insert) (Russian).

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External Links:

MathReview (H. A. Lauwerier)

Referenced by:

§7.14(iii).

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Certain integrals that contain a probability function and degenerate hypergeometric functions. Bul. Akad. S̆tiince RSS Moldoven 1969 (2), pp. 40–47 (Russian).

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MathReview (Wazir Hasan Abdi)

Referenced by:

§7.14(iii).

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Some integrals that contain a probability function and hypergeometric functions. Bul. Akad. Štiince RSS Moldoven 1970 (1), pp. 49–62 (Russian).

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MathReview (R. G. Langebartel)

Referenced by:

§7.14(iii).

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The Laplace transform for expressions that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).

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MathReview (L. Berg)

Referenced by:

§7.14(iii).

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Certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1975 (2), pp. 86–88, 95 (Russian).

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MathReview (C. Tanaka)

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§7.14(iii).

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9: Bibliography L

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Algorithm 344: Student’s t-distribution [S14]. Comm. ACM 12 (1), pp. 37–38.

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Single-precision Fortran, maximum accuracy 8S. For Remarks see same journal 13(1970), pp. 124 and 449.

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ISSN 0001-0782, Document, Remark 1 and Remark 2

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§8.28(iv).

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On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions. Constr. Approx. 10 (1), pp. 15–30.

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ISSN 0176-4276, Document, MathReview (P. Anandani), ZentralBlatt

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§8.13(i).

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Sur la distribution des nombres premiers. Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).

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ZentralBlatt

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§27.12.

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10: Bibliography C

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Ellipsoidal distributions of charge or mass. J. Mathematical Phys. 2, pp. 441–450.

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External Links:

MathReview (H. Bremekamp), ZentralBlatt

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§19.33(iv), §19.37(iv).

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Notes:

This library treats about 180 different mathematical functions, including a substantial collection of probability integrals, Bessel functions, and higher transcendental functions. Implementations in single, double, and quad precisions are provided. See Moshier (1989).

External Links:

GAMS (package CEPHES)

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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Algorithm AS 310. Computing the non-central beta distribution function. Appl. Statist. 46 (1), pp. 146–156.

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Single-precision Fortran.

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FullText, Code, ZentralBlatt

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2nd item.

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Calculation of angular distributions in complex angular momentum theories of elastic scattering. Molecular Physics 37 (6), pp. 1703–1712.

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Document

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§14.31(iii).

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Some non-central distribution problems in multivariate analysis. Ann. Math. Statist. 34 (4), pp. 1270–1285.

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External Links:

FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.4(i), §35.4(ii).

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