GenbetaII {VGAM} | R Documentation

## The Generalized Beta II Distribution

### Description

Density for the generalized beta II distribution with shape parameters `a` and `p` and `q`, and scale parameter `scale`.

### Usage

    dgenbetaII(x, scale = 1, shape1.a, shape2.p, shape3.q, log = FALSE)

### Arguments

`x` | vector of quantiles.

`shape1.a, shape2.p, shape3.q` | positive shape parameters.
`scale` | positive scale parameter.
`log` | Logical. If `log = TRUE` then the logarithm of the density is returned.

### Details

See `genbetaII`, which is the VGAM family function for estimating the parameters by maximum likelihood estimation. Several distributions, such as the Singh-Maddala, are special case of this flexible 4-parameter distribution. The product of `shape1.a` and `shape2.p` determines the behaviour of the density at the origin.

### Value

`dgenbetaII` gives the density.

### Author(s)

T. W. Yee

### References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.

### See Also

`genbetaII`.

### Examples

    dgenbetaII(0, shape1.a = 1/4, shape2.p = 4, shape3.q = 3)
    dgenbetaII(0, shape1.a = 1/4, shape2.p = 2, shape3.q = 3)
    dgenbetaII(0, shape1.a = 1/4, shape2.p = 8, shape3.q = 3)

[Package VGAM version 1.1-1 Index]