Beta Distribution

Parameters

Domain

Probability Density Function

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")