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How to plot continuous probability distributions (in Excel)

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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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We begin by creating the values that will be shown on the $x$-axis. These values depend not only on the distribution, but on which portion of it you wish to see.

For example, for an exponential distribution, the sample space is $(0,\infty)$, but for a standard normal distribution, it is the whole real line, and you may wish to view just $( - 5,5)$, or some other range.

In the example below, we will use a Gamma distribution with $\alpha = 5$ and $\beta = 5$, plotted on the range $\lbrack 0,50\rbrack$, but the particular example doesn’t matter; you can use the procedure below for any distribution.

To generate the $x$ values from 0 to 50, begin with just the first two values in the sequence, in this case 0 and 1, as shown below.

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Drag the small green square in the bottom right of the selection downward, to create a sequence that goes all the way up to 50. (Only the beginning of it is shown here.)

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If your sample spaces were a smaller range (say, just from -2 to 2), you would need to use smaller steps to get a smooth plot. For example, you might begin with -2 and -1.9 to tell Excel to take steps of size 0.1.

In the adjacent column, we put the formula for the distribution, based on the $x$ values in the first column. In this example, recall that we’ll plot a Gamma distribution with $\alpha = 5$ and $\beta = 5$, so we use the formula shown below. The final parameter for the distribution should always be FALSE, to indicate that we are not asking Excel for a cumulative distribution function, but just the usual probability density function.

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After typing your probability density function’s formula, drag it down the column.

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Highlight just column B and insert a line chart from the Insert tab on the Ribbon, as shown below.

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This will create a chart that does not yet include your desired $x$-axis labels; rather, the horizontal axis markings will be 1, 2, 3, 4, etc. To get the correct labels on the $x$-axis, right-click the chart and choose “Select Data…” This will bring up the window shown below.

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Click the Edit button for the Horizontal (Category) Axis Labels and select column A. Click OK twice to return to your plot, which should then have the correct $x$-axis labels. You can then update the chart title and axis labels to be more descriptive if desired, as shown in the final result, below.

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Although we used the GAMMA.DIST function in Excel, you can use any of the built-in continuous probability distribution functions, such as BETA.DIST, CHISQ.DIST, F.DIST, NORM.DIST, LOGNORM.DIST, or T.DIST.

Content last modified on 24 July 2023.

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