Norton (1984) presented a calculation of the MLE for the parameter of the double exponential distribution based on the calculus. An inductive approach is presented here.
Hurley, W. J.
"An Inductive Approach to Calculate the MLE for the Double Exponential Distribution,"
Journal of Modern Applied Statistical Methods: Vol. 8
, Article 25.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss2/25