# Math Help - Are these adequate estimators?

1. ## Are these adequate estimators?

Hi.
I was wondering whether $\overline{x}$, 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. Let´s assume f(x,a,b) to be the pdf of a continuous random variable that is conditional on parameters a and b.
Let´s 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).

Two Questions:
1) May I estimate a and b by estimating EV and VAR by $\overline{x}$ and s^2 respectively and then solve $\overline{x}$=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?