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How to plot discrete probability distributions (in R)

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There are many famous discrete probability distributions, such as the binomial and geometric distributions. How can we get access to them in software, to plot the distribution as a series of points?

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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.

The example below uses a geometric distribution (with $p=0.5$), whose sample space is ${0,1,2,3,\ldots}$. We specify that we just want to use $x$ values in the set ${0,1,2,\ldots,10}$. (In some software, the geometric distribution’s sample space begins at 1, but not in R.)

If you wanted to use a different distribution, you could replace dgeom with, for example, dbinom, adjusting the named parameters as appropriate.

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

xs = 0:8                     # choose the sample space (here, it's 0,1,2,...,10)
ys = dgeom( xs, prob=0.5 )   # compute the shape of the distribution
plot( xs, ys, type='p',      # plot circles...
      xlab='sample space', ylab='probability' )
segments( xs, 0, xs, ys )    # ...and lines

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (