The power-law relationship has been regarded as the fundamental
description of the size distribution from large-scale-earthquake to
small-scale-laboratory rock ruptures. However, deviation from the
power-law relationship has often been reported, especially when the
amplitude distribution is used for -value estimation in rock acoustic
emission testing, the effect of attenuation should be considered. Here,
we perform a detailed analysis on the deviation of the size distribution
from a power law and prove that the cumulative frequency distribution
will inevitably result in deviation from the power law. We also discuss
modification of the attenuation on the doubly truncated size
distribution from a more general perspective. We find that in a certain
interval, the attenuation will not modify the size distribution and the
-value is theoretically verified to be unchanged. Based on these
discussions, we propose a new -value estimation procedure for rock
acoustic emission testing and apply it to a dilation rupturing test, the
procedure exhibits good performance.