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# Cumulative Plot

A Cumulative Distribution is, mathematically speaking, the integral of the normalized probability density function. Practically speaking, a point on the cumulative distribution gives us the probability that a random variable will be LESS THAN OR EQUAL TO a specified value.

That is, if (X, Y) is a point on the cumulative distribution S-curve, then Y equals the probability that the random variable will be <= X.

To plot a Cumulative Distribution after a Probabilistic Analysis:

1. Select Statistics > Cumulative Plot
2. In the Cumulative Plot dialog:
1. Select the Data to Plot. The following data can be plotted:
1. The Factor of Safety, Weight, Required Support Pressure, Failure Depth, or Excavation Face Area for any analysis method which was used (these will be listed first before the input data Random Variables).
2. Any Random Variable that you have defined for the Probabilistic Analysis (these will appear after the pre-defined data types in the drop-down list of Data to Plot).
2. The Number of Bins used to create the plot can be customized if desired.
3. Select the Selection Method. The following blocks selection options are available:
1. Results Set: the available result sets include All Valid Blocks, Removable Blocks, and Failed Blocks for the selected Stage To Use
2. Currently Visible Blocks (Filtered Blocks): the blocks currently visible, determined by the current filter
3. Single Block: a single block given by the selected Block ID
4. Click Plot to generate the cumulative plot.
The sampled mean, standard deviation, minimum and maximum values for the data plotted will be listed at the bottom of the plot.

## Right-Click Options

Other options are available if you right-click on a Cumulative Plot. For example:

• Select the Change Plot Data option to change the data viewed on the plot.
• Plot in Excel: you can either right-click a chart or click the Plot in Excel button in the toolbar. An Excel application will open and the data will be exported in columns. A chart object duplicating what was in the RocTunnel3 will also appear.
• Copy Chart Image: this allows you to copy and paste the chart as an image.
• Copy Data to Clipboard: this allows you to copy and paste the data to other spreadsheet or word file.

Experiment with the different options available in the right-click menu.

## Chart Options

The Chart Options pane on the left side allows you to modify the graph with the drawing/settings of the plot. The drawing section allows you to change the labels while settings allow you to adjust the graph settings such as axis alignment, min/max, etc.