APPENDIX ASelected Distributions

This appendix describes a partial set of useful probability distributions, suggestions for when to use them, and how to replicate them for simulations in Excel. There is also a spreadsheet on this book’s website with all of these distributions already set up in Excel:

www.howtomeasureanything.com/cybersecurity

Distribution Name: Triangular

Schematic illustration of triangular distribution

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, as in 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 ...

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