PMID- 1910633
OWN - NLM
STAT- MEDLINE
DCOM- 19911118
LR  - 20190516
IS  - 0108-7673 (Print)
IS  - 0108-7673 (Linking)
VI  - 47 ( Pt 4)
DP  - 1991 Jul 1
TI  - Exact random-walk models in crystallographic statistics. VII. An all-space-group 
      study of the effects of atomic heterogeneity on the P.D.F.'s of magnitude of [E].
PG  - 336-40
AB  - Exact expressions have been found for the probability density functions 
      (p.d.f.'s) of the magnitude of the normalized structure factor for all the 
      two-dimensional and most three-dimensional space groups [Part VI: Rabinovich, 
      Shmueli, Stein, Shashua & Weiss (1991). Acta Cryst. A47, 328-335]. The results of 
      that investigation are used in the present article to examine some effects of 
      atomic heterogeneity, in the various space-group symmetries, on the p.d.f.'s. 
      Some typical comparisons are made between p.d.f.'s based on the central limit 
      theorem and p.d.f.'s computed from exact formulae. In addition, the exact results 
      are compared to histograms of simulated values of magnitude of [E]. It is found 
      that the p.d.f.'s for some space groups are influenced rather strongly by the 
      presence of outstandingly heavy scatters, but they are quite insensitive to the 
      presence of such scatterers in other space groups. The often made general 
      statement 'The presence of outstandingly heavy scatterers may invalidate the 
      indications of Wilson's statistics' is made more precise here, insofar as it 
      depends on the particular space group.
FAU - Rabinovich, S
AU  - Rabinovich S
AD  - Division of Computer Research and Technology, National Institutes of Health, 
      Bethesda, Maryland 20982.
FAU - Shmueli, U
AU  - Shmueli U
FAU - Stein, Z
AU  - Stein Z
FAU - Shashua, R
AU  - Shashua R
FAU - Weiss, G H
AU  - Weiss GH
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
PT  - Research Support, U.S. Gov't, Non-P.H.S.
PL  - United States
TA  - Acta Crystallogr A
JT  - Acta crystallographica. Section A, Foundations of crystallography
JID - 8305825
SB  - IM
MH  - Fourier Analysis
MH  - *Models, Chemical
MH  - Models, Statistical
MH  - *X-Ray Diffraction
EDAT- 1991/07/01 00:00
MHDA- 1991/07/01 00:01
CRDT- 1991/07/01 00:00
PHST- 1991/07/01 00:00 [pubmed]
PHST- 1991/07/01 00:01 [medline]
PHST- 1991/07/01 00:00 [entrez]
AID - 10.1107/s0108767390013319 [doi]
PST - ppublish
SO  - Acta Crystallogr A. 1991 Jul 1;47 ( Pt 4):336-40. doi: 10.1107/s0108767390013319.