  Half-lives of radionuclides span more than 50 orders of magnitude. We
characterize the probability distribution of this broad-range data set at the
same time that explore a method for fitting power-laws and testing
goodness-of-fit. It is found that the procedure proposed recently by Clauset et
al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the
power-law hypothesis even for power-law synthetic data. In contrast, we
establish the existence of a power-law exponent with a value around 1.1 for the
half-life density, which can be explained by the sharp relationship between
decay rate and released energy, for different disintegration types. For the
case of alpha emission, this relationship constitutes an original mechanism of
power-law generation.
