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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)

Domain

Four-Parameter Pearson 6 Distribution

Probability Density Function

Cumulative Distribution Function

Three-Parameter Pearson 6 Distribution

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("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).
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