I was wondering whether , which is an adequate estimator (i.e. unbiased...) of the expected value and s^2, which is an an adequate (s.a.) estimator of the variance of a random variable, are also adequate estimators for distribution parameters of densities which are not characterized by their mean and variance (i.e. the pareto distribution or the like)?
E.g. Letīs assume f(x,a,b) to be the pdf of a continuous random variable that is conditional on parameters a and b.
Letīs further assume the expected value and the variance are functions of those parameters a and b, i.e. EV=EV(a,b) and VAR=VAR(a,b).
1) May I estimate a and b by estimating EV and VAR by and s^2 respectively and then solve =EV(a,b) and s^2=VAR(a,b) for a and b?
2) May I substitute a and b within the pdf by terms of EV and VAR, to have the pdf be conditional on its EV and VAR instead of its less intuitive parameters a and b?
Thanks for answering.