A note on the Hendrickson-Lattman phase probability distribution and its equivalence to the generalized von Mises distribution
© Barnett and Kingston 2024.
| Veröffentlicht in: | Journal of applied crystallography. - 1998. - 57(2024), Pt 2 vom: 01. Apr., Seite 492-498 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2024
|
| Zugriff auf das übergeordnete Werk: | Journal of applied crystallography |
| Schlagworte: | Journal Article circular statistics computational crystallography crystallographic phase determination probability density functions |
| Zusammenfassung: | © Barnett and Kingston 2024. Hendrickson & Lattman [Acta Cryst. (1970), B26, 136-143] introduced a method for representing crystallographic phase probabilities defined on the unit circle. Their approach could model the bimodal phase probability distributions that can result from experimental phase determination procedures. It also provided simple and highly effective means to combine independent sources of phase information. The present work discusses the equivalence of the Hendrickson-Lattman distribution and the generalized von Mises distribution of order two, which has been studied in the statistical literature. Recognizing this connection allows the Hendrickson-Lattman distribution to be expressed in an alternative form which is easier to interpret, as it involves the location and concentration parameters of the component von Mises distributions. It also allows clarification of the conditions for bimodality and access to a simplified analytical method for evaluating the trigonometric moments of the distribution, the first of which is required for computing the best Fourier synthesis in the presence of phase, but not amplitude, uncertainty |
|---|---|
| Beschreibung: | Date Revised 11.04.2024 published: Electronic-eCollection Citation Status PubMed-not-MEDLINE |
| ISSN: | 0021-8898 |
| DOI: | 10.1107/S1600576724000311 |