HomeTechniques and Tips@RISK DistributionsLeft Skewed or Negative Skewed Log-normal Distribution

# 3.31. Left Skewed or Negative Skewed Log-normal Distribution

Applies to: @RISK 5.0 and newer

I want to create a left skewed (negatively skewed) log-normal distribution function with @RISK, using three percentiles. Using the @RISK Define Distribution window with alt parameters, I put in 0 as my 5th percentile, .018 as my 70th percentile, and .021 as my 95th percentile. But then the Define Distribution window says "Unable to graph distribution", and the function returns a #VALUE error. Can you explain why @RISK won't allow this to be done?

This is based on the definitions for skewness and the domains for mu and sigma in a log-normal (mu > 0 and sigma > 0, μ and σ both positive). The skewness will never be negative if all terms in the expression are always positive.

You do have several workarounds, however:

• Enter 100 minus the percents, minus the percentiles, and minus the RiskLognorm, like this:

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

The 95th percentile of 0.021 becomes a 5th percentile of minus 0.021, and so on for the others.  The RiskMakeInput wrapper tells @RISK to collect data and statistics on the final formula, not just the RiskLognorm. See also: All Articles about RiskMakeInput.

With this technique, the Define Distribution window will show the "backwards" log-normal, with the negative percentiles. But after a simulation, the Browse Results window will show the desired distribution with +0.021 in the 95th percentile.

• Enter those three (x,p) pairs in your worksheet and then fit a log-normal distribution. @RISK comes up with RiskLognorm(0.013156,0.0022747, RiskShift(0.0038144) ).

• You could also use a different distribution, such as the BetaGeneral distribution, which can take on the left skewed shape.