Pearson index

As Talias (2007) has pointed out, there is an interesting analogy between the Pearson Index and the Neyman-Pearson lemma. (The Pearsons in question are different. Alan Pearson is the author of the Pearson index and Egon Pearson, 1895-1980, was the son of Karl Pearson, 1857-1936 and the collaborator of Jerzey Neyman, 1894-1981, in developing hypothesis testing.) Both are relevant to optimizing a function subject to a constraint. In the case of the Pearson index this is profit subject to total cost, and for the Neyman-Pearson lemma it is power subject to the constraint of an overall type I error rate. In both cases a ratio plays a key role. For the Neyman-Pearson lemma this is the likelihood ratio and for the Pearson index the index itself is a ratio of expected profit to expected cost. 

For further discussion of the Pearson index in project management see Burman et al. (2007), Burman and Senn (2003), Regan and Senn (1997), Senn (1996, 1998a) and Senn and Rosati, 2002) for its relation to the Neyman-Pearson lemma see Talias (2007) and for real option theory see Dixit and Pyndick (1994). 

Talias MA (2007) Optimal decision indices for R D project evaluation in the pharmaceutical industry Pearson index versus Gittins index. European Journal of Operational Research 177 1105-1112. 

With the aid of the Pearson indexing the inverse path of the crystallographic classification is crossed, i.e., by reducing the classification of the chemical compounds to the set of 230 space groups to the number of 14 Bravais lattice, yet leaving open (like a variable) the total number of atoms present in the elementary cell, a number that varies from case to case. 

Accordingly, the Pearson classification is merely reductive than complete, as long as no parameter is specified, for example, the number of atoms per unit cell, which however varies. Overall, the Pearson indexing serves for an immediate view of the type of structure, at the same time indicating stoichiometric information for the unit cell. 

Fields can be utilized in virtual screening applications for assessing the similarity (alignment) or complementarity (docking) of molecules. Two similarity measures have achieved the most attention. These are the so-called Garbo- [195] and Hodgkin indexes [196] respectively. Others are Pearson s product moment correlation coefficient [169] and Spearman s rank correlation coefficient [169]. 

Pearson et al. (3) prepared high refractive index copolymerizable azo compounds, (III), which were used to prepare intraocular lenses. 

Crackel, R.L., Gray, J.I., Pearson, A.M., Booren, A.M., and Buckley. D.J. 1988. Some further observations on the TBA test as an index of lipid oxidation in meats. Food Chem. 28 187-196. 

The index usually indicates the sequence cubic (3), hexagonal (2), or double hexagonal (4) for the ABAC sequence. The Pearson symbols (Table 2.5) can clarify cases such as hexagonal structures with an ABC sequence and a = 3 for the index. The symbols t for tetragonal, o for orthorhombic, m for monoclinic, and h for hexagonal, rhombohedral, or trigonal indicate the type of distortion of an idealized structure. Without distortion, a = 3 is for a cubic structure and a = 2 is for a hexagonal (or rhombohedral) structure. 

Examples of mathematical methods include nominal range sensitivity analysis (Cullen Frey, 1999) and differential sensitivity analysis (Hwang et al., 1997 Isukapalli et al., 2000). Examples of statistical sensitivity analysis methods include sample (Pearson) and rank (Spearman) correlation analysis (Edwards, 1976), sample and rank regression analysis (Iman Conover, 1979), analysis of variance (Neter et al., 1996), classification and regression tree (Breiman et al., 1984), response surface method (Khuri Cornell, 1987), Fourier amplitude sensitivity test (FAST) (Saltelli et al., 2000), mutual information index (Jelinek, 1970) and Sobol s indices (Sobol, 1993). Examples of graphical sensitivity analysis methods include scatter plots (Kleijnen Helton, 1999) and conditional sensitivity analysis (Frey et al., 2003). Further discussion of these methods is provided in Frey Patil (2002) and Frey et al. (2003, 2004). 

Pearson s first index. A measure of the asymmetry of the distribution of the x variable, defined as ... 

Negative values show a right-tailed distribution, positive values a left-tailed distribution. Other measures of distribution asymmetry are Pearson s second index, skewness, and the Bonferroni index. 

Matthews correlation index = Pearson similarity coefficient —> classification parameters > maximal binding energy —> scoring functions (0 average binding energy)... 

Pearson s first index statistical indices (0 moment statistical functions)... 

Similarity coefficients for binary variables are also used as —> classification parameters for two-dass problems among these, the most used is the Pearson coeffident (Table S9), which is also known as Matthews correlation index. 

Most of the commonly used models compute a cation/anion equivalent balance, but even this information is seldom translated into error for any subsequent calculation. No codes currently incorporate known analytical precision into evaluation of the error and uncertainty of speciation, saturation index, or mass transfer calculations. Future codes such as INTERP (Appendix) or the expert system of Pearson and others described in this volume, should include an optimization routine which would calculate the propagation of these reported errors, and compute bounding values that clearly define the magnitude of uncertainty. 

Following the procedure previously described and briefly reported in the method section, we found (at PWP level) that the Fukui index associated with orbital lone pair of oxygen in sulfine, has the value of 0.04 eV, while those associated with carbon and sulphur, are 0.19 and 0.21 eV, respectively. Speaking in terms of hard-soft theory of Pearson, we can indicate the orbital with the lowest Fukui index as the most reactive in the electrophilic reaction with H" ". 

OrientExpress V3.3 freeware was used to index the Laue diffraction patterns. We developed a special algorithm to measure the sample-detector distance (d) and to determine the coordinates of the projection of the sample position in the recording plane of the CCD detector. The algorithm implies the analysis of two Laue diffraction patterns detected at two different distances dpi at the same angular position of the sample. A Pearson VII two-variable function was used to approximate the profiles of the Bragg reflections. 

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