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The statistics of the highest E value.

Grzegorz Chojnowski¹, Matthias Bochtler

¹International Institute of Molecular and Cell Biology, ul. Trojdena 4, 02-109 Warsaw, Poland.

Acta Crystallographica. Section A, Foundations of Crystallography

|June 16, 2007

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The highest normalized structure-factor amplitude (E value) in crystal structures follows a Gumbel-Fisher-Tippett distribution. This finding aids in identifying outliers in experimental diffraction data.

Area of Science:

Crystallography
X-ray Diffraction
Statistical Analysis

Background:

Previous work applied Gumbel-Fisher-Tippett (GFT) analysis to extreme reflection intensities.
This study extends GFT analysis to the highest normalized structure-factor amplitudes (E values).

Purpose of the Study:

To investigate the distribution, expectation value, and standard deviation of the highest E values.
To assess the applicability of GFT analysis to real crystal structure data.

Main Methods:

Separate analysis of acentric and centric reflections.
Assumption of random atom arrangement and neglect of E-value correlations.
Application of Gumbel-Fisher-Tippett extreme-value analysis.

Main Results:

Related Experiment Videos

The highest E value is approximately Gumbel-Fisher-Tippett distributed.
The root of the expectation value of the highest normalized intensity serves as a good estimate for the highest E value.
The derived formulas are useful for small-molecule and protein crystal structures, excluding data below 2.5 Å.

Conclusions:

GFT analysis provides a robust statistical framework for understanding highest E values in diffraction data.
The findings have practical implications for identifying outliers in experimental diffraction datasets.
This approach is applicable to both thin and thick resolution shells in crystal structures.