---
title: "Introduction - Cumulative probability plots"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575476/Introduction%20-%20Cumulative%20probability%20plots"
format: markdown
---
# Cumulative probability plots

  


The cumulative probability plot is a graphical representation of the<span style="color: #0b0125"> </span>[<span style="color: #0b0125">cumulative distribution function (cdf)</span>](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574886)<span style="color: #0b0125"> </span>sometimes just called the distribution function. It is the second most commonly used plot in risk analysis, after the [histogram](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575467). It is produced at the end of a Monte Carlo simulation by plotting each generated data value for a particular output on the x-axis against the fraction of all the generated values for that output that are less than or equal to that value. With a cumulative probability plot one can read off the probability of being above or below a particular value, or of being within, or outside, a particular range.

  


![image](media://3443a816-fef0-4218-b94d-5413514e0b6f)

  


For example, in the plot above, there is a 10% probability of being below $66000, a 50% probability of being below (or above) $96,000 and a 90% probability of being below $140,000. That also means an 80% probability of being between $66 000 and $140,000 and therefore a 20% probability of lying outside that range. At Epix Analytics, we tend to produce our own cdf plots in Excel (rather than Crystal Ball) by exporting the generated output values (select "Run" >> "Extract Data" >> Forecast Values" >> "OK") because we can customize them: for example, adding the dashed red lines and the triangle representing the distribution's mean in this plot.

  


**This section discusses the following:**

  


[Relationship between cdf and density (histogram) plots](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575474/Relationship+between+cdf+and+density+histogram+plots)

[Ascending and descending cumulative plots](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575478)

[Second-order cumulative probability plot](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575479)

[Plotting the cdf of a variable with discrete and continuous elements](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575471)

[Overlaying cdf plots](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575480)

[Stochastic dominance tests](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575481)

  


  


  


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