a) Hypothetical relationship between the best fit power law slope and the lower limit (x_min) for a stable power law fit. The flat region in the middle of the plot shows the range over which the fit is independent of the choice of x_min, i.e. stable. b) The same relationship as a) for the real GOES long channel peak flux frequency distribution derived with the standard GOES event list (start threshold = 40%, end threshold = 50%). It can be seen that there is no flat region where the power law slope is independent of choice of x_min. This suggests that the distribution may not be best approximated by a single power law.