Applies to: @RISK 5.0 and Up

Creating a Left-Skewed Lognormal Distribution in @RISK

Applies to: @RISK for Excel, all versions supporting alt parameters

 

Question:
Using the Define Distribution window with alt parameters and the data below:

• 5th percentile = 0

• 70th percentile = 0.018

• 95th percentile = 0.021

The Define Distribution window says "Unable to graph distribution", and the function returns #VALUE!.

Why won’t @RISK allow this?

Explanation:

The lognormal distribution is defined only for positive values of μ and σ (mu and sigma). Because all terms are always positive, a lognormal distribution cannot have negative skew. That is, its skewness is always positive.

Trying to create a left-skewed lognormal with your percentiles violates the mathematical domain, which is why @RISK cannot graph it or compute values.

Workarounds:

1. Use the “backwards” trick with RiskMakeInput
   Enter negative values for the RiskLognormAlt function and then wrap it in RiskMakeInput:

   =RiskMakeInput(-RiskLognormAlt(5%, -0.021, 30%, -0.018, 95%, 0))
   

   • The 95th percentile of 0.021 becomes a 5th percentile of -0.021, and so on.

   • RiskMakeInput tells @RISK to collect data and statistics on the final formula rather than the RiskLognorm alone.

   • The Define Distribution window will show the “backwards” lognormal.

   • After a simulation, Browse Results shows the distribution with +0.021 at the 95th percentile.

2. Fit a lognormal from percentiles
   Enter the three (x,p) pairs in your worksheet and fit a lognormal distribution. @RISK will calculate parameters such as:

   RiskLognorm(0.013156, 0.0022747, RiskShift(0.0038144))
   

   This achieves the desired left-skewed shape through a shifted lognormal.

3. Use an alternative distribution
   If the goal is left skewness, consider BetaGeneral or other flexible distributions. BetaGeneral can take a left-skewed shape without needing negative lognormal transformations.

 

Related Articles:

All Articles about RiskMakeInput

Fitting Distributions from Percentiles

BetaGeneral Distribution

Summary:
A lognormal distribution cannot be directly left-skewed due to its mathematical constraints. Use RiskMakeInput with negative percentiles, fit a shifted lognormal, or choose a different flexible distribution like BetaGeneral.