Probability density function:

Cumulative distribution function:

Mean:

Variance:

Median:

Generate a sample of pseudorandom numbers from a PERT distribution:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness:

For large λ, the modified PERT distribution becomes symmetric:

Limiting values:

Kurtosis:

For large λ, kurtosis nears the kurtosis of NormalDistribution:

Limiting values:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

Consistent use of Quantity in parameters yields QuantityDistribution:

Find the quartiles of the project completion time:

An expert estimates that a project that takes from 4 to 6 months to complete will take 5 months and 1 week:

The distribution of the project completion time:

Find the expected completion time and its standard deviation:

Find the probability of the project taking longer to complete:

Use PERTDistribution as a smooth alternative to TriangularDistribution:

PERT distribution is closed under translation and scaling by a positive factor:

Relationships to other distributions:

Default value of the shape parameter λ is 4:

PERT distribution is a transformation of BetaDistribution:

BetaDistribution with parameters and is a special case of PERTDistribution on the unit interval:

The equivalent PERT distribution is only valid for and :

PDFs for different c values with CDF contours: