# statistical applications

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##### 2: 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). …
##### 3: 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). …
##### 5: 7.20 Mathematical Applications
###### §7.20(iii) Statistics
7.20.1 $\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(t-m)^{2}/(2\sigma^{2})}\,% \mathrm{d}t=\frac{1}{2}\operatorname{erfc}\left(\frac{m-x}{\sigma\sqrt{2}}% \right)=Q\left(\frac{m-x}{\sigma}\right)=P\left(\frac{x-m}{\sigma}\right).$
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: Preface
The authoritative status of the existing Handbook, and its orientation toward applications in science, statistics, engineering and computation, will be preserved. …
##### 9: 26.19 Mathematical Applications
These have applications in operations research, probability theory, and statistics. …
##### 10: 20.12 Mathematical Applications
This ability to uniformize multiply-connected spaces (manifolds), or multi-sheeted functions of a complex variable (Riemann (1899), Rauch and Lebowitz (1973), Siegel (1988)) has led to applications in string theory (Green et al. (1988a, b), Krichever and Novikov (1989)), and also in statistical mechanics (Baxter (1982)).