Types of Distributions

There are a huge amount of statistical tools and machine learning models that assume a normal distribution. What is the normal distribution, what other distributions are out there. In this blog post I will describe some of the most common types of distributions.

Every distribution will either be discrete or continuous so it is important to define these two terms first.

A distribution that is discrete means that each event or trial is boolean. Think of rolling a die. When you roll a die you can have 1, 2, 3, 4, 5, or 6. However, you cannot roll a 1.9. Each outcome in a discrete distribution is clearly different from one another.

On the other hand, in a continuous distributions you can have outcomes that are indistinguishable from one another. A classic example is height. You may measure 6ft on one ruler, but on another ruler with more markings you may find that you are 5ft 11.999inches. These two numbers flow right into one another and therefore you want to use a range of values to define your result such as 5.5ft to 6ft.

It is also important to note that in a continuous distribution, each individual event actually has a probability of 0. When you take the probability of continuous distributions you are actually measuring the probability of a range of events such as the probability of being between 5ft 11in and 6ft, or the probability of being over 6ft tall.

A uniform distribution can either be discrete or continuous. In a uniform distribution, every event is equally likely to occur. If you think of the die again, each of the six outcomes has an equal probability of occurring at 1/6.

Should a uniform distribution be continuous, it can be graphed as a rectangle between points a and b with a height of 1/ (b-a). Remember that each individual event’s probability is not 1 / (b-a) but 0.

The binomial distribution is a type of discrete distribution. In this distribution we have n independent and identical Bernoulli trials. This means…

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