Is there a way to fit exponential decays with a Distribution of decay constants?

I have been doing some reading on fitting data using a distribution of decay constants instead of just 1 or 2 different single exponential decays. So instead of just y=ae^kx or y=ae^kx +be^cx, I would like to fit to a function where there is a gausian distribution of k's. Is this possible without customized programing in matlab? Phys. Chem. Chem. Phys., 2011, 13, 3819–3830