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Table 5 Statistical analysis of power-law parameters

From: Mapping small molecule binding data to structural domains

 

Frequency of Pfam domains

Ligands per Pfam domain family

Ligands per target

xmin

10

81

210

alpha

2.07

1.71

2.15

Goodness of fit

0.5

0.42

0.42

vs_lognormal

yes (p = 5.1*10^-9)

yes/no (p = 0.48)

yes/no (p = 0.57)

vs_exponential

yes (p = 3.9*10^-3)

yes (p = 0.10)

yes (p = 8.5 *10^-8)

vs_weibull

yes (p = 2.1*10^-4)

Yes/no (p = 0.16)

no (p = 1.0*10^-3)

magnitude

~ 3

~ 3

~ 1

support for power-law

yes

yes

no

  1. Parameters of the power-law functions fitted to the observed distributions of Pfam-A domain frequencies (left column), number of ligands associated with each Pfam-A domain (middle column) and number of ligands associated with individual targets (right column) are shown in columns 'xmin' and 'alpha'. 'Goodness of fit' indicates the p-Value calculated from a KS goodness of fit test. The rows vs_lognormal, vs_exponential, vs_weibull indicate outcomes of maximum-likelihood tests against alternative distributions. 'Yes' indicates significant support for a power-law distribution, 'no' indicates support for the alternative over a power-law. 'Magnitude' specifies the orders of magnitude in the distribution spanned by a power-law and 'support for power-law' is the summary outcome for each distribution.