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How to plot continuous probability distributions (in R)

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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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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 (