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# Beta Distribution

## Parameters

- continuous shape parameter ()
- continuous shape parameter ()
, - continuous boundary 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("Beta";Data;[Options]```1```) ``` Probability Density Function `BetaPdf(x,alpha1,alpha2,a,b)` ``` =BetaPdf(alpha1;alpha2;a;b) =DistPdf("Beta(alpha1;alpha2;a;b)";x) ``` Cumulative Distribution Function `BetaCdf(x,alpha1,alpha2,a,b)` ``` =BetaCdf(alpha1;alpha2;a;b) =DistCdf("Beta(alpha1;alpha2;a;b)";x) ``` Survival Function `BetaSurv(x,alpha1,alpha2,a,b)` ``` =DistSurv("Beta(alpha1;alpha2;a;b)";x) ``` Hazard Function `BetaHaz(x,alpha1,alpha2,a,b)` ``` =BetaHaz(alpha1;alpha2;a;b) =DistHaz("Beta(alpha1;alpha2;a;b)";x) ``` Cumulative Hazard Function `BetaCumHaz(x,alpha1,alpha2,a,b)` ``` =DistCumHaz("Beta(alpha1;alpha2;a;b)";x) ``` Inverse CDF (Quantile Function) `BetaInv(P,alpha1,alpha2,a,b)` ``` =BetaInv(alpha1;alpha2;a;b) =DistInv("Beta(alpha1;alpha2;a;b)";P) ``` Random Numbers `BetaRand(alpha1,alpha2,a,b)` ``` =BetaRand(alpha1;alpha2;a;b) =DistRand("Beta(alpha1;alpha2;a;b)") ``` Mode `BetaMode(alpha1,alpha2,a,b)` ``` =DistMode("Beta(alpha1;alpha2;a;b)") ``` Mean `BetaMean(alpha1,alpha2,a,b)` ``` =BetaMean(alpha1;alpha2;a;b) =DistMean("Beta(alpha1;alpha2;a;b)") ``` Variance `BetaVar(alpha1,alpha2,a,b)` ``` =BetaVar(alpha1;alpha2;a;b) =DistVar("Beta(alpha1;alpha2;a;b)") ``` Standard Deviation `BetaStdev(alpha1,alpha2,a,b)` ``` =BetaStdev(alpha1;alpha2;a;b) =DistStdev("Beta(alpha1;alpha2;a;b)") ``` Skewness `BetaSkew(alpha1,alpha2,a,b)` ``` =DistSkew("Beta(alpha1;alpha2;a;b)") ``` (Excess) Kurtosis `BetaKurt(alpha1,alpha2,a,b)` ``` =DistKurt("Beta(alpha1;alpha2;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")