Applies to:
@RISK 4.x and Up
RISKOPTIMIZER 1.x–5.x

How do I choose α1 and α2 for a BetaGeneral distribution to get a desired mean and standard deviation?

Can I do this for other statistics or distributions?

 

Answer:
You generally can’t just enter α1 and α2 directly from mean and SD; you must solve for them. In @RISK 5.5+ you can:

1. Use JohnsonMoments if you want to target mean, SD, skewness, or kurtosis.

2. Use Alt. Parameters to specify percentiles instead of parameters—@RISK calculates the necessary α1/α2 automatically.

3. If you need a specific BetaGeneral mean and SD:

• Set up α1 and α2 as adjustable cells in Excel.

• Use formulas for the distribution’s mean and SD in other cells.

• Minimize the difference between desired and calculated statistics using RISKOptimizer or Excel Solver.

This approach works for other distributions too, provided you can express the target statistic as a function of the distribution parameters. Make sure to respect parameter constraints (e.g., α1, α2 > 0).

Example:
Start with α1 = α2 = 1. The calculated mean and SD may deviate from desired values. RISKOptimizer adjusts α1 and α2 until the distribution matches the target mean and SD as closely as possible.

You can also target mode, kurtosis, skewness, or other moments by adjusting formulas and constraints accordingly. For distributions with >2 parameters, add extra adjustable cells and constraints.

 

Attachments:
FindDistributionParams.xls