Method of moments (statistics)

Okay kiddo, let's imagine that you have a basket of different sized toys, but you don't know their sizes yet. You want to figure out how big each toy is using something called "method of moments".

First, you count how many toys you have in total and write it down. Then, you take one of the toys and measure how big it is with a ruler. This measurement is like a "moment" of information about the toy.

Next, you take another toy and measure its size too. You keep doing this until you've measured the size of all the toys in your basket. Now, you have many "moments" of information about the toys - one for each of their sizes.

But how do you figure out what the average size of all the toys is based on these moments? This is where "method of moments" comes in. You take all the moments you collected and use them to find the "moments" of some mathematical formula that describes the distribution of toy sizes. Then, you set the two sets of "moments" equal to each other and solve for the formula.

Now, you have a formula that tells you what the average size of the toys in your basket is, based on the moments you collected. You can use this formula to estimate the size of any toy you haven't measured yet, or you can use it to make predictions about other baskets of toys with similar distributions.

So there you have it kiddo, method of moments is a way to use information about individual measurements to estimate the properties of a distribution. Just like how you used different moments of toy sizes to figure out their average size!