This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

PERTDistribution

PERTDistribution
represents a PERT distribution with range min to max and maximum at c.
PERTDistribution
represents a modified PERT distribution with shape parameter .
  • PERTDistribution is used for project completion time analysis within PERT (program evaluation and review technique) and is effectively a reparametrized BetaDistribution.
  • PERTDistribution allows min, max, and c to be any real numbers such that and is any non-negative real number.
Probability density function:
Cumulative distribution function:
Mean:
Variance:
Median:
Probability density function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=
 
Cumulative distribution function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=
 
Mean:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Variance:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Median:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
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:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
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:
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:
New in 8