Edgeworth

It has been known for a long time (Edgeworth [1887]) that minimizing of the linear sums of deviations... 

Draper NR, Smith H (1981) Applied regression techniques, 2nd edn. Wiley, New York Edgeworth FY (1887) On observations relating to several quantities. Hermathena 6 279... 

Miller, R. S., S. H. Frankel, C. K. Madnia, andP. Givi (1993). Johnson-Edgeworth translation for probability modeling of binary scalar mixing in turbulent flows. Combustion Science and Technology 91, 21-52. 

Edgeworth, F. Y. 1907. On the representation of statistical frequency by a series. J. Royal Statistical Society, Series A. 70 102-6. 

A second statistical expansion that may be used to describe the atomic probability distribution is due to Edgeworth (Kendal and Stuart 1958, Johnson 1969). It expresses a distribution in terms of its cumulants k. If D is the differential operator, P(u) is described as... 

This formulation, referred to as the Edgeworth approximation (Zucker and... 

Another way to derive the dimensionless groups needed for scale-up purposes has been proposed by Edgeworth and Thring (1957). The general concept is that the differential equations that describe the process could be used, since they are known for most processes that are relevant to chemical engineering. The main problem is that many of these equations cannot be easily integrated or are very difficult to be handled, in general. 

Edgeworth, R., Thring, M.W., Joint Symposium The Scaling-Up of Chemical Plant and Processes, London (1957)... 

More complex mathematical treatment is necessary when the thermal motion is very large, as for hydrogen atoms in a room-temperature neutron structure analysis, or when it is curvilinear as in a hindered-rotor. The Uy second-rank tensor does not adequately describe the nuclear or electron-scattering density when the motion is far from harmonic or when it deviates from the familiar ellipsoidal probability form. Tb deal with such examples, more complex mathematic expressions using Gram Charlier or Edgeworth expansions are available [210]. 

Edgeworth, Maria. Letters for Literary Ladies. Joseph Milligan, George Town. 1810. 

Davis D. R. and FarineUa P. (1997) Collisional evolution of Edgeworth-Kuiper Belt objects. Icarus 125, 50-60. 

FarineUa P., Davis D. R., and Stem S. A. (2000) Formation and collisional evolution of the Edgeworth-Kuiper Belt. In Protostars and Planet IV (eds. V. Mannings, A. P. Boss, and S. S. Russell), University of Arizona Press, Tucson, pp. 1255-1282. 

Solid N2, CH4, H2O, and CO have been found on Triton and Pluto, witli additional CO2 on Triton. The molecule N2 dominates both surfaces, and other molecules are trapped in an N2 matrix. The only molecule identified on Charon is H2O. Surface compositions of these two bodies are quite different from those of satellites of Jupiter, Saturn, and Uranus. The compositional relationsliip of Triton and Pluto to that of tlie Edgeworth-Kuiper belt objects, and to tlie comets, is still unclear. 

Bodleian Library Oxford, MS Dep. cl 35/1 Anna Maria Beddoes to Mrs. Edgeworth, 31 July 1812. 

The similar Edgeworth-Cramer asymptotic expansion may offer abetter approximation [4] usually it is truncated like... 

In addition to the EMG fimction, many other mathematical models have been suggested to accoimt for the profiles of experimental peaks and to determine characteristic shape-parameters, such as a number of theoretical plates, a skew and an excess. These parameters are related to the second, third and fourth moments (Eq. 6.77) of the peak, respectively. For example, the Gram-Charlier series (GC) [96,114,115] and the Edgeworth-Cramer series (EC) [115,116] have been... 

For multi-objective optimization, theoretical background has been laid, e.g., in Edgeworth (1881) Koopmans (1951) Kuhn and Tucker (1951) Pareto (1896, 1906). Typically, there is no unique optimal solution but a set of mathematically incomparable solutions can be identified. An objective vector can be regarded as optimal if none of its components (i.e., objective values) can be improved without deterioration to at least one of the other objectives. To be more specific, a decision vector x S and the corresponding objective vector f(x ) are called Pareto optimal if there does not exist another x G S such that / (x) < /j(x ) for alH = 1,..., A and /j(x) < /j(x ) for at least one index j. In the MCDM literature, widely used synonyms of Pareto optimal solutions are nondominated, efficient, noninferior or Edgeworth-Pareto optimal solutions. 

Edgeworth, F. Y. (1881). Mathematical Psychics An Essay on the Application of Mathematics to the Moral Sciences (C. Kegan Paul Co., London), University Microfilms International (Out-of-Print Books on Demand), 1987. 

Edgeworth JA, Farmer M, Sicilia A, Tavares P, Beck J, Campbell T, Lowe J, Mead S, Rudge P, Collinge J, Jackson GS (2011) Lancet 377 487... 

Shapes of molecular electronic bands are studied using the methods of the statistical theory of spectra. It is demonstrated that while the Gram-Charlier and Edgeworth type expansions give a correct description of the molecular bands in the case of harmonic-oscillator-like potentials, they are inappropriate if departure from harmonicity is considerable. The cases considered include a set of analytically-solvable model potentials and the numerically exact potential of the hydrogen molecule. 

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