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How to Measure Anything in Cybersecurity Risk by Stuart McClure, Daniel E. Geer Jr., Richard Seiersen, Douglas W. Hubbard

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Appendix A Selected Distributions

Distribution Name: Triangular

Graph: horizontal axis of 0-5 million has line ascending up to point between 3-4 million, descending to 5 million forming triangular shape. 90% of area marked for graph.

Figure A.1 Triangular Distribution

Parameters:

  • UB (Upper bound)
  • LB (Lower bound)
  • Mode—this may be any value between UB and LB.

Note that UB and LB are absolute outer limits—a 100% CI.

For a triangular distribution, the UB and LB represent absolute limits. There is no chance that a value could be generated outside of these bounds. In addition to the UB and LB, this distribution also has a mode that can vary to any value between the UB and LB. This is sometimes useful as a substitute for a lognormal, when you want to set absolute limits on what the values can be but you want to skew the output in a way similar to a lognormal. It is useful in any situation where you know of absolute limits but the most likely value might not be in the middle, like the normal distribution.

  • When to Use: When you want control over where the most likely value is compared to the range, and when the range has absolute limits.
  • Examples: Number of records lost if you think the most likely number is near the top of the range and yet you have a finite number of records you know cannot be exceeded.
  • Excel Formula:

    numbered Display Equation
  • Mean: = (LB+Mode+UB)/3

Distribution Name: Binary

Figure A.2 Binary Distribution

Parameters:

  • P (Event probability)

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