International Tables for Crystallography (2006). Vol. B, ch. 2.1, pp. 190-209   | 1 | 2 |

Chapter 2.1. Statistical properties of the weighted reciprocal lattice

Chapter index

Assumption of independence
Assumption of uniformity,
Atomic characteristic functions
Average intensity
of general reflections 2.1.2
of zones and rows 2.1.3
Average multiples for point groups
Beta distribution
first kind
second kind
Central-limit theorem
Lindeberg–Lévy version
effect of
Characteristic functions,
Correction-factor approach 2.1.7,
Crystallographic statistics
Cumulant-generating functions
Cumulative distribution functions
Delta functions
Distribution function
beta, first kind
beta, second kind
ideal acentric
ideal centric
non-ideal 2.1.7, 2.1.8
of sums, averages and ratios 2.1.6
probability density 2.1.4
probability density, ideal 2.1.5
Effect of centring
Fourier approach
Fourier–Bessel series
Fourier method 2.1.8
Gamma distribution
General reflections, average intensity of 2.1.2
Hypersymmetric distributions
Ideal acentric distributions
Ideal centric distributions
Ideal probability density distributions 2.1.5
Independence, assumption of
Lindeberg–Lévy version of the central-limit theorem
Meijer's G function
Non-ideal distributions 2.1.7, 2.1.8
Non-ideal probability density functions
of |E|
Non-independent variables
Partially bicentric arrangement
Periodic delta functions
Point groups
average multiples for
Probability density distributions 2.1.4
ideal 2.1.5
Probability density functions
of |E|, non-ideal
Random-walk problem
exact solution 2.1.8
Reciprocal lattice
weighted, statistical properties of 2.1.1
Statistical properties of the weighted reciprocal lattice 2.1.1
Structure factors
trigonometric, even absolute moments of
trigonometric, moment of
Subcentric arrangement
Trigonometric structure factors
even absolute moments of
moment of
Uniformity, assumption of,
Weighted reciprocal lattice
statistical properties of 2.1.1
Zones and rows, average intensity of 2.1.3