Probability distributions in R

Last updated on 2024-03-12 | Edit this page

Estimated time: 12 minutes

Overview

Questions

  • How can I calculate probabilities in R?

Objectives

  • Demonstrate and practice the use of the base R functions for calculating probabilities.
  • Explain the concept of cumulative distribution.

Before we look at more distributions, let’s get some hands-on experience in R!
R knows a whole range of distributions: Here is a list of them.

For each distribution, R has four different function calls: For the binomial distribution, these all end with binom:
- dbinom: density
- pbinom: cumulative distribution function (percentage of values smaller than)
- qbinom: quantile function (inverse of cumulative distribution)
- rbinom: generates random numbers

The first letter specifies if we want to look at the density, probability distribution/mass function, quantile or random numbers. The suffix specifies the distribution.

The arguments depend on the distribution we are looking at, but always include the parameters of that function.

Calculating probabilities

Let’s use the example where we caught 10 frogs and count how many of them are light-colored.

For known parameters, we can calculate the the chances of counting exactly 5 light-colored frogs:

R 

n = 10 # number of frogs we catch
p = 0.3 # true fraction of light frogs
dbinom(x=5, size=n, prob=p)

OUTPUT 

[1] 0.1029193

We can ask for the probability of catching at most 5 light frogs. In this case, we need the cumulative probability distribution starting with p:

R 

pbinom(q=5, size=n, prob=p) # at most

OUTPUT 

[1] 0.952651

Similarly, we can ask for the probability of catching more than 5 light frogs:

R 

pbinom(q=5, size=n,prob=p, lower.tail=FALSE) # larger than

OUTPUT 

[1] 0.04734899

Catching at least 5 light frogs is a rare event.

Challenge: Disease prevalence

There is a disease with a known prevalence of 4%. You have a group of 100 randomly selected persons. Use the above functions to calculate

  1. the probability of seeing exactly 7 persons with the disease.
  2. the probability of seeing at least 7 persons with the disease.
  1. Exactly 7 persons:

R 

dbinom(x=7,size=100,prob=0.04)

OUTPUT 

[1] 0.05888027
  1. At least 7 persons:

R 

pbinom(q=6, size=100, prob=0.04, lower.tail=FALSE)

OUTPUT 

[1] 0.1063923