In statistics and econometrics, the generalized beta distribution (or GB) is a family of continuous probability distributions of positive random variables with five parameters. The GB distribution includes as special or limiting cases such popular distributions as the beta (both first and second kinds), chi-squared, gamma, F, half-normal, and uniform distributions, among others. The generalized beta distribution allows for considerable flexibility in statistical modeling and testing.
Quick Facts Parameters, Support ...
Generalized Beta (GB)
Probability density function |
Cumulative distribution function |
Parameters |
(kurtosis) (real) (scale) (real) (domain) (real) (shape) (real) (shape) (real) |
---|
Support |
|
---|
PDF |
|
---|
CDF |
no closed form |
---|
Mean |
(see hypergeometric series) |
---|
Median |
no closed form |
---|
Mode |
for |
---|
Variance |
where is the mean. |
---|
Skewness |
where is the mean and is the variance. |
---|
Excess kurtosis |
see text |
---|
Entropy |
see text |
---|
MGF |
|
---|
CF |
;\alpha +\beta ;i\,t)\!}
(see Confluent hypergeometric function) |
---|
Close