International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 7.5, pp. 666-676
https://doi.org/10.1107/97809553602060000608

Chapter 7.5. Statistical fluctuations

A. J. C. Wilsona‡

aSt John's College, Cambridge CB2 1TP, England

References

First citationAbramowitz, M. & Stegun, I. A. (1964). Handbook of mathematical functions. National Bureau of Standards Publication AMS 55.Google Scholar
 First citationBoer, J. L. de (1982). Statistics of recorded counts. Crystallographic statistics, edited by S. Ramaseshan, M. F. Richardson & A. J. C. Wilson, pp. 179–186. Bangalore: Indian Academy of Sciences.Google Scholar
 First citationEastabrook, J. N. & Hughes, J. W. (1953). Elimination of dead-time corrections in monitored Geiger-counter X-ray measurements. J. Sci. Instrum. 30, 317–320.Google Scholar
 First citationFrench, S. & Wilson, K. (1978). On the treatment of negative intensity observations. Acta Cryst. A34, 517–525.Google Scholar
 First citationGrant, D. F. (1973). Single-crystal diffractometer data: the on-line control of the precision of intensity measurement. Acta Cryst. A29, 217.Google Scholar
 First citationHirshfeld, F. L. & Rabinovich, D. (1973). Treating weak reflexions in least-squares calculations. Acta Cryst. A29, 510–513.Google Scholar
 First citationKillean, R. C. G. (1967). A note on the a priori estimation of R factors for constant-count-per-reflection diffractometer experiments. Acta Cryst. 23, 1109–1110.Google Scholar
 First citationKillean, R. C. G. (1972). The a priori optimization of diffractometer data to achieve the minimum average variance in the electron density. Acta Cryst. A28, 657–658.Google Scholar
 First citationKillean, R. C. G. (1973). Optimization of scan procedure for single-crystal X-ray diffraction intensities. Acta Cryst. A29, 216–217.Google Scholar
 First citationMack, M. & Spielberg, N. (1958). Statistical factors in X-ray intensity measurements. Spectrochim. Acta, 12, 169–178.Google Scholar
 First citationMackenzie, J. K. & Williams, E. J. (1973). The optimum distribution of counting times for determining integrated intensities with a diffractometer. Acta Cryst. A29, 201–204.Google Scholar
 First citationOlkha, G. S. & Rathie, P. N. (1971). On a generalized Bessel function and an integral transform. Math. Nachr. 51, 231–240.Google Scholar
 First citationPaciorek, W. A. & Chapuis, G. (1994). Generalized Bessel functions in incommensurate structure analysis. Acta Cryst. A50, 194–203.Google Scholar
 First citationParrish, W. (1956). X-ray intensity measurements with counter tubes. Philips Tech. Rev. 17, 206–221.Google Scholar
 First citationPrince, E. & Nicholson, W. L. (1985). The influence of individual reflections on the precision of parameter estimates in least squares refinement. Structure & statistics in crystallography, edited by A. J. C. Wilson, pp. 183–195. Guilderland, NY: Adenine Press.Google Scholar
 First citationShmueli, U. (2001). Editor. International tables for crystallography. Vol. B. Reciprocal space, 2nd ed. Dordrecht: Kluwer Academic Publishers.Google Scholar
 First citationShoemaker, D. P. (1968). Optimization of counting times in computer-controlled X-ray and neutron single-crystal diffractometry. Acta Cryst. A24, 136–142.Google Scholar
 First citationShoemaker, D. P. & Hamilton, W. C. (1972). Further remarks concerning optimization of counting times in single-crystal diffractometry: rebuttal to Killean; consideration of background counting and slewing times. Acta Cryst. A28, 408–411.Google Scholar
 First citationSkellam, J. G. (1946). The frequency distribution of the difference between two Poisson values belonging to different populations. J. R. Stat. Soc. 109, 296.Google Scholar
 First citationSzabó, P. (1978). Optimization of the measuring time in diffraction intensity measurements. Acta Cryst. A34, 551–553.Google Scholar
 First citationThomsen, J. S. & Yap, F. Y. (1968). Simplified method of computing centroids of X-ray profiles. Acta Cryst. A24, 702–703.Google Scholar
 First citationWerner, S. A. (1972a). Choice of scans in X-ray diffraction. Acta Cryst. A28, 143–151.Google Scholar
 First citationWerner, S. A. (1972b). Choice of scans in neutron diffraction. Acta Cryst. A28, 665–669.Google Scholar
 First citationWilson, A. J. C. (1967). Statistical variance of line-profile parameters. Measures of intensity, location and dispersion. Acta Cryst. 23, 888–898.Google Scholar
 First citationWilson, A. J. C. (1978). On the probability of measuring the intensity of a reflection as negative. Acta Cryst. A34, 474–475.Google Scholar
 First citationWilson, A. J. C. (1980). Relationship between `observed' and `true' intensity: effect of various counting modes. Acta Cryst. A36, 929–936.Google Scholar
 First citationWilson, A. J. C., Thomsen, J. S. & Yap, F. Y. (1965). Minimization of the variance of parameters derived from X-ray powder diffractometer line profiles. Appl. Phys. Lett. 7, 163–165.Google Scholar
 First citationWright, E. M. (1933). On the coefficients of power series having exponential singularities. J. London Math. Soc. 8, 71–79.Google Scholar
 First citationZevin, L. S., Umanskii, M. M., Kheiker, D. M. & Panchenko, Yu. M. (1961). K voprosu o difraktometricheskikh priemah pretsizionnyh izmerenii elementarnyh yacheek. Kristallografiya, 6, 348–356.Google Scholar