R in a Nutshell

Normal Distribution

As an example, we’ll start with the normal distribution. As you may remember from statistics classes, the probability density function for the normal distribution is:

To find the probability density at a given value, use the dnorm function:

dnorm(x, mean = 0, sd = 1, log = FALSE)

The arguments to this function are fairly intuitive: x specifies the value at which to evaluate the density, mean specifies the mean of the distribution, sd specifies the standard deviation, and log specifies whether to return the raw density (log=FALSE) or the logarithm of the density (log=TRUE). As an example, you can plot the normal distribution with the following command:

> plot(dnorm, -3, 3, main = "Normal Distribution")

The plot is shown in Figure 17-1.

Figure 17-1. Normal distribution

The distribution function for the normal distribution is pnorm:

pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)

You can use the distribution function to tell you the probability that a randomly selected value from the distribution is less than or equal to q. Specifically, it returns p = Pr(x ≤ q). The value q is specified by the argument q, the mean by mean, and the standard deviation by sd. If you would like the raw value p, then specify log.p=FALSE; if you would like log(p), then specify log.p=TRUE ...