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# Kumaraswamy Distribution

## Parameters

- continuous shape parameter ()
- continuous shape parameter ()
, - continuous boundary parameters ( < )

where

## Worksheet and VBA Functions

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

 Description VBA Functions Worksheet Functions Distribution Fitting - ``` =DistFit("Kumaraswamy";Data;[Options]```1```) ``` Probability Density Function `KumaraswamyPdf(x,alpha1,alpha2,a,b)` ``` =KumaraswamyPdf(alpha1;alpha2;a;b) =DistPdf("Kumaraswamy(alpha1;alpha2;a;b)";x) ``` Cumulative Distribution Function `KumaraswamyCdf(x,alpha1,alpha2,a,b)` ``` =KumaraswamyCdf(alpha1;alpha2;a;b) =DistCdf("Kumaraswamy(alpha1;alpha2;a;b)";x) ``` Survival Function `KumaraswamySurv(x,alpha1,alpha2,a,b)` ``` =DistSurv("Kumaraswamy(alpha1;alpha2;a;b)";x) ``` Hazard Function `KumaraswamyHaz(x,alpha1,alpha2,a,b)` ``` =KumaraswamyHaz(alpha1;alpha2;a;b) =DistHaz("Kumaraswamy(alpha1;alpha2;a;b)";x) ``` Cumulative Hazard Function `KumaraswamyCumHaz(x,alpha1,alpha2,a,b)` ``` =DistCumHaz("Kumaraswamy(alpha1;alpha2;a;b)";x) ``` Inverse CDF (Quantile Function) `KumaraswamyInv(P,alpha1,alpha2,a,b)` ``` =KumaraswamyInv(alpha1;alpha2;a;b) =DistInv("Kumaraswamy(alpha1;alpha2;a;b)";P) ``` Random Numbers `KumaraswamyRand(alpha1,alpha2,a,b)` ``` =KumaraswamyRand(alpha1;alpha2;a;b) =DistRand("Kumaraswamy(alpha1;alpha2;a;b)") ``` Mode `KumaraswamyMode(alpha1,alpha2,a,b)` ``` =DistMode("Kumaraswamy(alpha1;alpha2;a;b)") ``` Mean `KumaraswamyMean(alpha1,alpha2,a,b)` ``` =KumaraswamyMean(alpha1;alpha2;a;b) =DistMean("Kumaraswamy(alpha1;alpha2;a;b)") ``` Variance `KumaraswamyVar(alpha1,alpha2,a,b)` ``` =KumaraswamyVar(alpha1;alpha2;a;b) =DistVar("Kumaraswamy(alpha1;alpha2;a;b)") ``` Standard Deviation `KumaraswamyStdev(alpha1,alpha2,a,b)` ``` =KumaraswamyStdev(alpha1;alpha2;a;b) =DistStdev("Kumaraswamy(alpha1;alpha2;a;b)") ``` Skewness `KumaraswamySkew(alpha1,alpha2,a,b)` ``` =DistSkew("Kumaraswamy(alpha1;alpha2;a;b)") ``` (Excess) Kurtosis `KumaraswamyKurt(alpha1,alpha2,a,b)` ``` =DistKurt("Kumaraswamy(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")