Generalized normal distribution

Imagine you have a big bag of marbles of different sizes. Some marbles are bigger than others and some are smaller. And imagine you want to know how many marbles are a certain size. To find out, you could weigh them all and see how many weigh the same amount.

In this analogy, the size of the marbles represents a variable in a mathematical equation. And just like the bag of marbles, the variable can take on different values. So, we need to figure out how many times each value occurs.

This is where the Generalized Normal Distribution comes in. It's like a pattern that helps us estimate how often each value occurs. It's called "generalized" because it can apply to many different types of variables, not just size or weight.

The formula for this pattern includes three numbers: mu, sigma, and alpha. Mu represents the average value of the variable, sigma represents the spread, or how much the values vary from the average, and alpha represents the shape of the curve.

Using this formula, we can create a graph that shows the frequency of each value. It's like a bar graph, but instead of bars, we use lines to show the curve of the pattern. The peak of the curve represents the most common value, or mode, and the curve gets smaller on either side, showing how much less common values are.

So, the Generalized Normal Distribution is a pattern that helps us estimate how frequently different values occur in a variable. It takes into account the average, spread, and shape of the data, and creates a graph that shows the frequency of each value.