# The Method Of Moments (MOM)

## Method of Moments

### Method of moments

#### Introduction

If we have \(k\) parameters to estimate, we can solve this if we have \(k\) equations.

We generate these

First, we link each first \(k\) moments to functions of the parameters.

Then we replace the momenets with sample estimates.

#### Estimation

The moments of this population distribution are:

\(\mu_i =E[X^i]=g_i(\theta_1,...,\theta_k)\)

We have a sample.

\(X=[X_1,...,X_n]\)

We now define the method of moments estimator

\(\hat \mu_i=\dfrac{1}{n}\sum_{j=1}^nx_j^i\)