# The beta-PERT Distribution

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## Using the PERT Analysis Toolbar

Like the triangular distribution, the PERT distribution emphasizes the "most likely" value over the minimum and maximum estimates. However, unlike the triangular distribution the PERT distribution constructs a smooth curve which places progressively more emphasis on values around near the most likely value, in favor of values around the edges.

In practice, this means that we "trust" the estimate for the most likely value, and we believe that even if it is not exactly accurate as estimates seldom are , we have an expectation that the resulting value will be close to that estimate. Examples of the PERT distribution: Values near the peak are more likely than values near the edges.

Assuming that many real-world phenomena are normally distributed, the appeal of the PERT distribution is that it produces a curve similar to the normal curve in shape, without knowing the precise parameters of the related normal curve. The histogram below demonstrates the PERT distribution. Edit the parameter values and click "Redraw" to regenerate the distribution. The triangular distribution is more precise, but the PERT distribution may better reflect real-world phenomena.

When the distribution is symmetrical — when the mode is half-way between the minimum and maximum — it looks like a normal distribution try 0, 10 and Moving the mode skews the distribution try 0, 10, and The simple case of the PERT distribution takes a minimum, maximum, and most likely value.

But use of the scale parameter is optional. If omitted, the default scale value is 4, which produces a curve that reasonably approximates the normal distribution.

P , uses the same distribution but takes as parameters the 10th and 90th percentile values. You would ordinarily use this function if your estimates exclude the tail or most unlikely probabilities. The PERT distribution is a special case of the beta distribution that takes three parameters: Unlike the triangular distribution, the PERT distribution uses these parameters to create a smooth curve that fits well to the normal or lognormal distributions.

Sampling from the beta distribution requires minimum and maximum values scale and two shape parameters, v and w. The PERT distribution uses the mode or most likely parameter to generate the shape parameters v and w. For more information and a more detailed analysis, see e. Toggle navigation Risk AMP.

Modeling Expert Data In project or cost planning, you often receive estimates of expected time, cost, or other variables. The Uniform Distribution The uniform distribution is the simplest possible distribution for sampling a range of estimates. The Triangular Distribution If you have a "most likely" estimate in addition to the minimum and maximum estimates, you can use this additional information to construct a probability distribution that favors the most likely value.

The PERT Distribution The PERT distribution also uses the most likely value, but it is designed to generate a distribution that more closely resembles realistic probability distribution. The changes are mainly under the hood. We fixed some small bugs and made quite a few changes leading up to the ability to choose custom colors in Tom's Planner for your time blocks and group headers.

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