  We investigate the effectiveness of the Inverse Laplace Transform (ILT)
analysis method to extract the distribution of relaxation rates from nuclear
magnetic resonance data with stretched exponential relaxation.
Stretched-relaxation is a hallmark of a distribution of relaxation rates, and
an analytical expression exists for this distribution for the case of a
spin-1/2 nucleus. We compare this theoretical distribution with those extracted
via the ILT method for several values of the stretching exponent and at
different levels of experimental noise. The ILT accurately captures the
distributions for $\beta \lesssim 0.7$, and for signal to noise ratios greater
than $\sim 40$; however the ILT distributions tend to introduce artificial
oscillatory components. We further use the ILT approach to analyze stretched
relaxation for spin $I>1/2$ and find that the distributions are accurately
captured by the theoretical expression for $I=1/2$. Our results provide a solid
foundation to interpret distributions of relaxation rates for general spin $I$
in terms of stretched exponential fits.
