Time histories of the normalised relative count rate excess of GLEs. The origin of the time axis is the start of the GLE, and the time is normalised by the time to maximum. Top: Individual GLEs, as noted in the right margin, plotted with different colours. The curve with a large excess in the decay phase is GLE 2000 Jul 14 (see text). Bottom: Median of the profiles in the top panel (plus signs, which merge into a continuous fat line before the rise and in the decay) plus and minus its mean absolute deviation (grey vertical bars). The median was in addition smoothed over 55 points (time step 0.55 units) to reduce noise, and normalised to unity. The red solid line is the best fit of a modified Weibull function to the median profile. The dashed lines show the fit plus and minus an analytically estimated statistical uncertainty (see text, Eqs. (3) and (4)).