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# Johnson SU Distribution

## Parameters

- continuous shape parameter
- continuous shape parameter ()
- continuous scale parameter ()
- continuous location parameter

## Cumulative Distribution Function

where ,  and is the Laplace Integral.

## Worksheet and VBA Functions

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

 Description VBA Functions Worksheet Functions Distribution Fitting - ``` =DistFit("JohnsonSU";Data) ``` Probability Density Function `JohnsonSUPdf(x,gamma,delta,lambda,xi)` ``` =JohnsonSUPdf(gamma;delta;lambda;xi) =DistPdf("JohnsonSU(gamma;delta;lambda;xi)";x) ``` Cumulative Distribution Function `JohnsonSUCdf(x,gamma,delta,lambda,xi)` ``` =JohnsonSUCdf(gamma;delta;lambda;xi) =DistCdf("JohnsonSU(gamma;delta;lambda;xi)";x) ``` Survival Function `JohnsonSUSurv(x,gamma,delta,lambda,xi)` ``` =DistSurv("JohnsonSU(gamma;delta;lambda;xi)";x) ``` Hazard Function `JohnsonSUHaz(x,gamma,delta,lambda,xi)` ``` =JohnsonSUHaz(gamma;delta;lambda;xi) =DistHaz("JohnsonSU(gamma;delta;lambda;xi)";x) ``` Cumulative Hazard Function `JohnsonSUCumHaz(x,gamma,delta,lambda,xi)` ``` =DistCumHaz("JohnsonSU(gamma;delta;lambda;xi)";x) ``` Inverse CDF (Quantile Function) `JohnsonSUInv(P,gamma,delta,lambda,xi)` ``` =JohnsonSUInv(gamma;delta;lambda;xi) =DistInv("JohnsonSU(gamma;delta;lambda;xi)";P) ``` Random Numbers `JohnsonSURand(gamma,delta,lambda,xi)` ``` =JohnsonSURand(gamma;delta;lambda;xi) =DistRand("JohnsonSU(gamma;delta;lambda;xi)") ``` Mean `JohnsonSUMean(gamma,delta,lambda,xi)` ``` =JohnsonSUMean(gamma;delta;lambda;xi) =DistMean("JohnsonSU(gamma;delta;lambda;xi)") ``` Variance `JohnsonSUVar(gamma,delta,lambda,xi)` ``` =JohnsonSUVar(gamma;delta;lambda;xi) =DistVar("JohnsonSU(gamma;delta;lambda;xi)") ``` Standard Deviation `JohnsonSUStdev(gamma,delta,lambda,xi)` ``` =JohnsonSUStdev(gamma;delta;lambda;xi) =DistStdev("JohnsonSU(gamma;delta;lambda;xi)") ``` Skewness `JohnsonSUSkew(gamma,delta,lambda,xi)` ``` =DistSkew("JohnsonSU(gamma;delta;lambda;xi)") ``` (Excess) Kurtosis `JohnsonSUKurt(gamma,delta,lambda,xi)` ``` =DistKurt("JohnsonSU(gamma;delta;lambda;xi)") ```