R Functions for Probability Distributions

Every distribution that R handles has four functions. There is a root name, for example, the root name for the normal distribution is norm. This root is prefixed by one of the letters

• p for “probability”, the cumulative distribution function (c. d. f.)
• q for “quantile”, the inverse c. d. f.
• d for “density”, the density function (p. f. or p. d. f.)
• r for “random”, a random variable having the specified distribution

For the normal distribution, these functions are pnorm, qnorm, dnorm, and rnorm. For the binomial distribution, these functions are pbinom, qbinom, dbinom, and rbinom. And so forth.

R has functions to handle many probability distributions. The table below gives the names of the functions for each distribution and a link to the on-line documentation that is the authoritative reference for how the functions are used. But don’t read the on-line documentation yet. First, try the examples in the sections following the table.

Normal Distribution

The normal distribution is the most commonly used distribution in statistics. This tutorial explains how to work with the normal distribution in R using the functions dnorm, pnorm, rnorm, and qnorm.

Prep data

pnorm

dnorm

qnorm

rnorm