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# Pert Distribution

## Parameters

(most likely value) - continuous mode parameter ()
, - continuous boundary parameters ( < )

## Description

The Pert distribution is a special case of the Beta distribution specified by the parameters

## Cumulative Distribution Function

where is the Beta Function,  and is the Regularized Incomplete Beta Function.

## Worksheet and VBA Functions

The following worksheet and VBA functions are available for this distribution:

 Description VBA Functions Worksheet Functions Distribution Fitting - ``` =DistFit("Pert";Data;[Options]```1```) ``` Probability Density Function `PertPdf(x,m,a,b)` ``` =PertPdf(m;a;b) =DistPdf("Pert(m;a;b)";x) ``` Cumulative Distribution Function `PertCdf(x,m,a,b)` ``` =PertCdf(m;a;b) =DistCdf("Pert(m;a;b)";x) ``` Survival Function `PertSurv(x,m,a,b)` ``` =DistSurv("Pert(m;a;b)";x) ``` Hazard Function `PertHaz(x,m,a,b)` ``` =PertHaz(m;a;b) =DistHaz("Pert(m;a;b)";x) ``` Cumulative Hazard Function `PertCumHaz(x,m,a,b)` ``` =DistCumHaz("Pert(m;a;b)";x) ``` Inverse CDF (Quantile Function) `PertInv(P,m,a,b)` ``` =PertInv(m;a;b) =DistInv("Pert(m;a;b)";P) ``` Random Numbers `PertRand(m,a,b)` ``` =PertRand(m;a;b) =DistRand("Pert(m;a;b)") ``` Mode `PertMode(m,a,b)` ``` =DistMode("Pert(m;a;b)") ``` Mean `PertMean(m,a,b)` ``` =PertMean(m;a;b) =DistMean("Pert(m;a;b)") ``` Variance `PertVar(m,a,b)` ``` =PertVar(m;a;b) =DistVar("Pert(m;a;b)") ``` Standard Deviation `PertStdev(m,a,b)` ``` =PertStdev(m;a;b) =DistStdev("Pert(m;a;b)") ``` Skewness `PertSkew(m,a,b)` ``` =DistSkew("Pert(m;a;b)") ``` (Excess) Kurtosis `PertKurt(m,a,b)` ``` =DistKurt("Pert(m;a;b)") ```

1. The `Options` parameter is optional. Possible options:
• "a=value"  (example: "a=0")
• "b=value"  (example: "b=10")
• "a=value1;b=value2"  (example: "a=2;b=8")