How to plot continuous probability distributions (in R)

Task

There are many famous continuous probability distributions, such as the normal and exponential distributions. How can we get access to them in software, to plot the distribution as a curve?

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Solution

Because R is designed for use in statistics, it comes with many probability distributions built in. A list of them is online here.

The challenge with plotting a random variable is knowing the appropriate sample space, because some random variables have sample spaces of infinite width, which cannot be plotted.

But we can just ask R to show us the central 99.98% of a continuous distribution, which is almost always indistinguishable to the human eye from the entire distribution.

We will use a normal distribution with $\mu=10$ and $\sigma=5$, but if you wanted to use a different distribution, you could replace qnorm and dnorm with, for example, qchisq and dchisq (for the $\chi^2$ distribution), adjusting the named parameters as appropriate. (For a list of supported distributions, see the link above.)

We style the plot below so that it is clear the sample space is continuous.

xmin <- qnorm( 0.0001, mean=10, sd=5 )  # compute min x as the 0.0001 quantile
xmax <- qnorm( 0.9999, mean=10, sd=5 )  # compute max x as the 0.9999 quantile
xs <- seq( xmin, xmax, length.out=100 ) # create 100 values in that range
ys <- dnorm( xs, mean=10, sd=5 )        # compute the shape of the distribution
plot( xs, ys, type='l' )                # plot that shape as a smooth line

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (ncarter@bentley.edu)