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, p. 666

Whatever the radiation, in both singlecrystal and powder diffractometry, the integrated intensity of a reflection is obtained as a difference between a counting rate averaged over a volume of reciprocal space intended to include the reflected intensity and a counting rate averaged over a neighbouring volume of reciprocal space intended to include only background. If these intentions are not effectively realized, there will be a systematic error in the measured intensity, but in any case there will be statistical fluctuations in the counting rates. The two basic modes (Parrish, 1956) are fixedtime counting and fixedcount timing. In the first, counts are accumulated for a predetermined time interval, and the variance of the observed counting rate is proportional to the true (mean) counting rate. In the second, on the other hand, the counting is continued until a predetermined number of counts is reached, and the variance of the observed counting rate is proportional to the square of the true counting rate. Put otherwise, the relative error in the intensities goes down inversely as the square root of the intensity for fixedtime counting, whereas it is independent of the intensity for fixedcount timing. Each mode has advantages, depending on the purpose of the measurements, and numerous modifications and compromises have been proposed in order to increase the efficiency of the use of the available time. References to some of the many papers are given in Section 7.5.7.
In principle, probability distributions can be determined for any postulated counting mode. In practice, they become complicated for all but the simplest modes; this is true even for the single measurement of the total counting rate or the background counting rate, but is even more pronounced for the distribution of their difference (the reflectiononly rate). For most crystallographic purposes, however, it is only necessary to know the mean (to correct for bias, if present) and the variance (for the estimation of weights in refinement processes, see Part 8 ) of the distribution function.
References
Parrish, W. (1956). Xray intensity measurements with counter tubes. Philips Tech. Rev. 17, 206–221.