Cumulative Distribution

The Cumulative distribution is used to define custom continuous distributions. You define the distribution by specifying [cumulative probability, value] pairs. A given pair (defined by a Prob. Level and a Value) implies that the cumulative probability of the Value is equal to the specified Prob. Level:

In this example, the cumulative probability of the value being less than or equal to 4 is 90%.

You add and remove pairs using the Add and Remove buttons (new pairs are inserted below the selected pair). In addition, if you place the cursor in the grid, the following hotkeys can be used:

Keys	Action
Ctrl+Enter	creates a new row below the cursor
Ctrl+Shift+Enter	creates a new row above the cursor
Ctrl+Backspace	deletes the current row

By definition, the first cumulative probability specified must be 0 and the last cumulative probability specified must be 1. The Prob. Level and the Value of the pairs cannot decrease as you move downward through the list. If the Prob. Levels decrease as you move down the table, GoldSim will sort the rows so that they are in increasing order when you close the dialog or press Apply. If the Values decrease as you move downward, GoldSim will warn you and ask you to fix the distribution.

Note: Specifying two or more Prob Levels with the same number results in a horizontal line in the CDF. Specifying two or more Values with the same number results in a vertical line in the CDF (and an infinite spike in the PDF).

You can also define the distribution as a log-cumulative (by checking the Log box). Whereas in a cumulative distribution, the density between values is constant (i.e., the distribution between values is uniform), in a log-cumulative, the density of the log of the value is constant (i.e., the distribution between values is log-uniform). If Log is checked, all Values for the distribution must be positive. Log-Cumulative distributions are often applied to quantities with large (order-of-magnitude) uncertainties.

Note: The values and cumulative probabilities must be entered as numbers and cannot be specified using links or expressions. The values are assumed to be entered in the Display Units for the element.

Note: You can copy and paste the entries for a Cumulative distribution from a spreadsheet. To do so, select the two columns in the spreadsheet (Probability Level and Value), and copy them to the clipboard. Then place the cursor in the upper left-hand corner of the grid (i.e., the first Probability Level) and paste (by pressing Ctrl+V).