BUILT-IN MATHEMATICA SYMBOL

PERTDistribution

represents a PERT distribution with range min to max and maximum at c.

PERTDistribution

represents a modified PERT distribution with shape parameter

.

MORE INFORMATION

PERTDistribution is used for project completion time analysis within PERT (program evaluation and review technique) and is effectively a reparametrized BetaDistribution.

PERTDistribution is also known as beta-PERT distribution.

PERTDistribution is equivalent to TransformedDistribution[min+x(max-min), xBetaDistribution[1+, 1+]].

PERTDistribution allows min, max, and c to be any real numbers such that and is any non-negative real number.

PERTDistribution can be used with such functions as Mean, CDF, and RandomVariate.

EXAMPLES

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Basic Examples (5)

Probability density function:

Cumulative distribution function:

Mean:

Variance:

Median:

Probability density function:

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Cumulative distribution function:

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Mean:

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Variance:

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Median:

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Scope (7)

Generate a set of pseudorandom numbers that are PERT distributed:

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

, the modified PERT distribution becomes symmetric:

Limiting values:

Kurtosis:

For large

, 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:

Applications (2)

An expert estimates that a project which 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:

Properties & Relations (7)

Parameter influence on the CDF for each

:

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

Relationships to other distributions:

PERTDistribution with shape parameter simplifies to PERTDistribution:

PERT distribution is a transformation of BetaDistribution:

BetaDistribution is a special case of PERTDistribution on unit interval:

BetaDistribution is a special case of PERTDistribution with shape parameter: