When to apply which discrete statistical distribution?

Statistics is an amazing subject which offers wide variety of statistical distributions to make predictions or to do forecasting. There are some discrete distributions which are defined for discrete random variables like number of telephone calls on a telephone exchange or number of children in a family. Some well celebrated discrete distributions are Binomial, Poisson, Geometric, Hypergeometric etcetera. On the other hand, we have continuous distributions like Normal, Beta, Gamma, Exponential etcetera which are defined for continuous random variables like lifetime of an electric bulb.

In this blog, my objective is to let readers know when to apply which discrete statistical distribution. Here, I go.

1. Bernoulli / Binomial Distribution: When there are only two outcomes of an experiment like failure or success, then we use Bernoulli distribution if the experiment has been performed only once. If same experiment is repeated finite number of times with constant probability of success then it becomes Binomial. It is applied when sampling is done using simple random sampling with replacement so that probability of success remains constant. Example: For calculating probability of observing 3 heads if a fair coin is tossed 10 times.
2. Poisson Distribution: This distribution is generally used for the count data of rare events when probability of success or happening of an event is very small. Example: for calculating probability of falling of a ceiling fan , probability of an accident on a traffic free road, probability of observing x number of typos in a page of a book published by well known publisher etcetera.
3. Geometric Distribution: This distribution is applied when someone is waiting for the first success to happen. Example: when someone is waiting for getting first head if he/she keeps on tossing a coin until he/she gets a head. simple!
4. Negative Binomial Distribution: This is just an extension of the Geometric distribution. Here, someone is waiting for the rth success to happen. Example: If someone is waiting for getting two heads when experiment of tossing a coin is performed.
5. Hypergeometric Distribution: This distribution is applied when sampling is done without replacement. Example: if a bag contains M red balls and N while balls and a person draws n balls without replacement, then for calculating the probability of getting r red balls out of n balls, Hypergeometric distribution can be used.

I hope you would find this blog informative. Thanks for reading my blog!