statistics

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1: Robb J. Muirhead

… … ►in Statistics were awarded by the University of Adelaide in 1967 and 1970, respectively. ►Muirhead’s main research interests are multivariate statistical analysis, statistical modeling, Bayesian statistics, and pharmaceutical statistics. His book Aspects of Multivariate Statistical Theory was published by John Wiley & Sons in 1982. … ►He is also an elected Fellow of the Institute for Mathematical Statistics, and an elected Member of the International Statistical Institute. …

2: Ingram Olkin

… … ► 2016) was Professor Emeritus of Statistics and Education in the Department of Statistics at Stanford University, California. … ► in mathematical statistics, Columbia University, New York, and Ph. … in mathematical statistics, University of North Carolina. … ► Royal Statistical Society. …

3: Jim Pitman

… … ► 1949 in Tasmania) is a professor in the departments of statistics and mathematics at the University of California, Berkeley. …Pitman held a position in the Department of Mathematics and Mathematical Statistics at the University of Cambridge, England. …in statistics from the Australian National University, Canberra, and a Ph. …in probability and statistics from Sheffield University. …

4: 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)).

5: 8.23 Statistical Applications

§8.23 Statistical Applications

►The functions

P\left(a,x\right)

and

Q\left(a,x\right)

are used extensively in statistics as the probability integrals of the gamma distribution; see Johnson et al. (1994, pp. 337–414). …The function

\mathrm{B}_{x}\left(a,b\right)

and its normalization

I_{x}\left(a,b\right)

play a similar role in statistics in connection with the beta distribution; see Johnson et al. (1995, pp. 210–275). …

6: Donald St. P. Richards

… … ► 1955 in Mandeville, Jamaica) is Professor, and Associate Head of the Department of Statistics, at the Pennsylvania State University, University Park, Pennsylvania. ►Richards has published numerous papers on special functions of matrix argument, harmonic analysis, multivariate statistical analysis, probability inequalities, and applied probability. … ►Richards was elected a Fellow of the Institute of Mathematical Statistics in 1998. He is also Associate Editor of the Annals of Statistics, Associate Review Editor of the Journal of the American Statistical Association, and Member of the Board of Governors of the Institute for Mathematics and its Applications. …

7: 35.9 Applications

§35.9 Applications

… ►See James (1964), Muirhead (1982), Takemura (1984), Farrell (1985), and Chikuse (2003) for extensive treatments. ►For other statistical applications of

{{}_{p}F_{q}}

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). … ►For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations). The asymptotic approximations of §35.7(iv) are applied in numerous statistical contexts in Butler and Wood (2002). …

8: 32.16 Physical Applications

… ►

Statistical Physics

►Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. …

9: 26.20 Physical Applications

… ►The latter reference also describes chemical applications of other combinatorial techniques. ►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). For an application of statistical mechanics to combinatorics, see Bressoud (1999). …

10: 32 Painlevé Transcendents

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