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# Pearson Type 6 Distribution

## Parameters

- continuous shape parameter ()
- continuous shape parameter ()
- continuous scale parameter ()
- continuous location parameter ( yields the three-parameter Pearson 6 distribution)

## Three-Parameter Pearson 6 Distribution

### 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("Pearson6";Data;[Options]```1```) ``` Probability Density Function `Pearson6Pdf(x,alpha1,alpha2,beta,[gamma])` ``` =Pearson6Pdf(alpha1;alpha2;beta;[gamma]) =DistPdf("Pearson6(alpha1;alpha2;beta;[gamma])";x) ``` Cumulative Distribution Function `Pearson6Cdf(x,alpha1,alpha2,beta,[gamma])` ``` =Pearson6Cdf(alpha1;alpha2;beta;[gamma]) =DistCdf("Pearson6(alpha1;alpha2;beta;[gamma])";x) ``` Survival Function `Pearson6Surv(x,alpha1,alpha2,beta,[gamma])` ``` =DistSurv("Pearson6(alpha1;alpha2;beta;[gamma])";x) ``` Hazard Function `Pearson6Haz(x,alpha1,alpha2,beta,[gamma])` ``` =Pearson6Haz(alpha1;alpha2;beta;[gamma]) =DistHaz("Pearson6(alpha1;alpha2;beta;[gamma])";x) ``` Cumulative Hazard Function `Pearson6CumHaz(x,alpha1,alpha2,beta,[gamma])` ``` =DistCumHaz("Pearson6(alpha1;alpha2;beta;[gamma])";x) ``` Inverse CDF (Quantile Function) `Pearson6Inv(P,alpha1,alpha2,beta,[gamma])` ``` =Pearson6Inv(alpha1;alpha2;beta;[gamma]) =DistInv("Pearson6(alpha1;alpha2;beta;[gamma])";P) ``` Random Numbers `Pearson6Rand(alpha1,alpha2,beta,[gamma])` ``` =Pearson6Rand(alpha1;alpha2;beta;[gamma]) =DistRand("Pearson6(alpha1;alpha2;beta;[gamma])") ``` Mode `Pearson6Mode(alpha1,alpha2,beta,[gamma])` ``` =DistMode("Pearson6(alpha1;alpha2;beta;[gamma])") ``` Mean `Pearson6Mean(alpha1,alpha2,beta,[gamma])` ``` =Pearson6Mean(alpha1;alpha2;beta;[gamma]) =DistMean("Pearson6(alpha1;alpha2;beta;[gamma])") ``` Variance `Pearson6Var(alpha1,alpha2,beta,[gamma])` ``` =Pearson6Var(alpha1;alpha2;beta;[gamma]) =DistVar("Pearson6(alpha1;alpha2;beta;[gamma])") ``` Standard Deviation `Pearson6Stdev(alpha1,alpha2,beta,[gamma])` ``` =Pearson6Stdev(alpha1;alpha2;beta;[gamma]) =DistStdev("Pearson6(alpha1;alpha2;beta;[gamma])") ``` Skewness `Pearson6Skew(alpha1,alpha2,beta,[gamma])` ``` =DistSkew("Pearson6(alpha1;alpha2;beta;[gamma])") ``` (Excess) Kurtosis `Pearson6Kurt(alpha1,alpha2,beta,[gamma])` ``` =DistKurt("Pearson6(alpha1;alpha2;beta;[gamma])") ```

1. The `Options` parameter is optional. Possible options: "gamma=value"  (example: "gamma=0")
2. The `gamma` parameter is optional (the default value is 0).