Method of moments /Point Estimation

<Method of moments>

Method of moments is a method for parameter estimations, especially called as a method of 'point estimation.'

As the name of the method implies. we can estimate unknown parameters with moments, specifically, population moments and sample moments. 

We can find parameters by equating rth population moments to rth sample moment. 

Then as n goes to infinity, sample moment converges to population moment in probability.

Then how many equations do we need? 

We can find R number of parameters by equating from the first population moments to Rth population moment with the first sample moment to Rth sample moment.  

<Examples for A parameter estimation>

We need a equation here. 

<Examples for two parameters estimation>

We need two equations here.