Discrete Distributions in R

Two common probabilities you will calculate in statistics is P(X = x) and P(X ≤ x). R provides your some simple ways to calculate these probabilities. In this article, we will learn how to calculate probabilities for Discrete Distributions in R.

The PDF

To calculate P(X = x), we can use the density functions. R has many functions for this all prefixed with d. For example, we can use dbinom to calculate the binomial distribution.

dbinom(7, size = 100, prob = 0.5)

## [1] 1.262774e-20

The above shows us the P(X = 7) when X is from a Bin(100, .5) distribution.

The CDF or Probability Mass Function

To calculate the probability that an item is less than x or P(X ≤ x), we can use the probability mass function, or the CDF. R has many methods all prefixed with p. For example, we can use pbiom for the binomial distribution.

pbinom(7, size = 10, prob = 0.5)

## [1] 0.9453125

The above shows us the P(X ≤ 7) when X is from a Bin(10, .5) distribution.

The Quantile or the Inverse CDF

Next, we can take a look at getting the quantile from a distribution. This is also known as the inverse CDF. To do this, we can use the distribution functions prefixed with a q. In our case, we will use qbinom.

qbinom(0.9453125, size = 10, prob = 0.5)

## [1] 7

In the above example, we put in the P(X ≤ 7) which we got from our previous example. We can see the value returned is 7 which is the value of X we used in our pdf.

Generating Random Binomials

We can also generate random samples from any of the distributions. Again, we follow the same pattern of having a short name for the distribution, i.e. binom, preceded by a prefix, r. To generate random samples, we can use rbinom.

rbinom(10, size =  10, prob = .5)

##  [1] 2 3 8 6 9 6 4 6 4 7

The example above will generate a random sample, which is multiple values of X from a Bin(10, .5) distribution. In our case, we supplied 10 as the first argument, thus our sample size will be 10.

Other Distributions

R provides many other continuous distributions with the same structure as above. Here is a list of many distributions and their respective functions.