**Many people are aware of the normal distribution or “bell curve”. What are some other probability distributions and when are they useful?**

You can think of a probability distribution as a collection of the number of times something happened. For example, how many students get which grade (70%, 73%, 94%, etc). We can visualize this type of information using a bar graph or histogram.

The normal distribution is nice because its symmetrical. However, many things are not symmetrical. Imagine the number of people that get a certain range of income. Since you can’t make less than $0 there is a lower boundary, but there is no upper boundary. This makes the distribution *skewed.*

You can think of this as a skewed normal distribution, but this doesn’t mean much mathematically. There are other probability distributions with other shapes for situations that are not symmetrical.

**Binomial Distribution**

This is probably the second most popular distribution. The binomial distribution is based on the chance that something occurs, such as flipping a coin and getting heads or tails, or rolling a die. The binomial distribution is discrete, meaning it only uses whole numbers.

**Gamma Distribution **

This distribution would be a better fit for income data, since with certain parameters it can be very skewed. Since it is so flexible, it is often used in Bayesian statistics to define a prior distribution. **See my introduction to Bayesian statistics here**.

**Beta Distribution**

The beta distribution is similar to the gamma in that it is very flexible, but it is only defined between 0 to 1. It is useful in Bayesian statistics when you are looking at binomial data since the chance something occurs is always between 0 and 1.

**Cauchy Distribution**

The Cauchy distribution is my favorite because its mean does not exist! If your data came from a cauchy distribution, it would not converge to an average value. Data like this are highly variable. Chemical chromatograms are like this, since so many variables influence the data.