This version of SPERT-Beta adds a new set of probability curves — only they’re not curves! Now, if the most likely outcome is equal to, or very close to, either the minimum or maximum point-estimates, the skew analysis will determine that a triangular distribution is the best shaped distribution for the uncertainty (and a right triangle, at that). This means that for a right-skewed uncertainty where the minimum point-estimate is also the most likely outcome, the implied shape of the probability distribution is a right triangle sloping downward to the right. Conversely, if the most likely outcome is equal to, or very close to, the maximum point-estimate, the skew analysis determines that the shape is a left-skewed, right triangle sloping downward to the left.
However, because the estimator can make a subjective opinion about how likely the most likely outcome really is, the actual shape of the implied distribution could be something other than a triangle. For near certainty, for example, the shape is flat along the x-axis and rises very sharply either towards the minimum or maximum point-estimates (depending on whether the most likely outcome is equal to or very near to the minimum or maximum point-estimate). For conditions where there is something less than medium-low confidence, the shape is concave and at the point of a guesstimate, the shape is virtually uniform.
So, if you want a triangular distribution, specify medium-low confidence, which approximates a right triangle. However, because of the way this template is constructed, it isn’t a perfectly-shaped right triangle — it’s close, but results at the range midpoint appear to differ by about 2%. For a perfect triangle, the beta value for medium-low confidence would need to be equal to 2, not 1.9. It’s set by default as 1.9 for medium-low confidence because medium-low confidence puts about 27% of the area under the curve to the small side of the curve at the 3-point range’s midpoint; a triangular distribution would put exactly 25% of the area under the curve on the small side of the range midpoint. To keep the triangular skew consistent with the meaning of all other skew values (like “near certainty” or “high confidence”), I opted to accept that the SPERT-Beta template won’t actually create probabilities for a perfectly-shaped, right triangle.
Try it out! As complicated as I described this enhancement to the SPERT-Beta template, it’s extremely easy to use still. Just enter a 3-point estimate, and set the most likely outcome to be equal to either the minimum point-estimate or the maximum point-estimate. Once you do that, the skew analysis will say “Triangular” and the alpha shape parameter will be set accordingly.
(Visit the Download page to download the latest version of Statistical PERT – Beta Edition).