Power-law + cut-off seems to correspond to a pdf like $f(x; \alpha, \lambda) = Cx^{-\alpha}e^{-\lambda x}$
Thus, you should find the maximum likelihood estimator of both $\alpha , \lambda$. This can be done sequentially (i. e. once you find the ML estimator of $\alpha$ then you insert it in the likelihood function and find $\hat{\lambda}_{ML}$.\hat{\lambda}_{ML}$). They do not seem very difficult to obtain, see Kay book first volume for maybe some help. If there is no closed form solution use numerical methods (see http://en.wikipedia.org/wiki/Expectation-maximization_algorithm ) 1 Power-law + cut-off seems to correspond to a pdf like$f(x; \alpha, \lambda) = Cx^{-\alpha}e^{-\lambda x}$Thus, you should find the maximum likelihood estimator of both$\alpha , \lambda$. This can be done sequentially (i. e. once you find the ML estimator of$\alpha$then you insert it in the likelihood function and find$\hat{\lambda}_{ML}\$.