RiskPearson6

Description

 

RiskPearson6(alpha1,alpha2,beta)  specifies a Pearson type VI distribution with shape parameters alpha1 and alpha2, and scale parameter beta.

 

Examples

 

RiskPearson6(5,1,2) returns a Pearson type VI distribution with shape parameters 5 and 1, and scale parameter 2.

RiskPearson6(D3,E3,F3) returns a Pearson type VI distribution with shape parameters taken from cells D3 and E3, and scale parameter from cell F3.

 

Guidelines

All parameters, alpha1, alpha1, and beta, must be positive.

Parameters

α1 continuous shape parameter α1 > 0
α2 continuous shape parameter α2 > 0
β continuous scale parameter β > 0

Domain

0 ≤ x < +∞ continuous

Density and Cumulative Distribution Functions

 

F(x) has no closed form.

 

Here, β is the Beta Function.

 

Mean

 

for α2 > 1

Variance

 

for α2 > 2

 

Skewness

 

for α2 > 3

 

Kurtosis

 

for α2 > 4

 

Mode

 

for α1 > 1

 

0

otherwise

Examples