$$f_{c_1,c_2}(x)=\begin{cases}\frac{c_1c_2^{c_1}}{x^{1-c_1}}\ \forall x\leq c_2\\0\ \ \ \ \text{elsewere}.\end{cases}$$
I am given the density function above, from which we are are asked to compute the Gini coefficient. That part I got. But then we are asked to "propose a method of moment estimator for the Gini coefficient".
I know how to compute a method of moment with respect to my density function. But I do not understand what it means to propose a method of moments for a coefficient.
I am also asked to compute the maximum likelihood estimator, and I know as a property that in this case, the result is invariant from the $\theta$ chosen, is it the same for the method of moments ?