invlomax {VGAM} | R Documentation

## Inverse Lomax Distribution Family Function

### Description

Maximum likelihood estimation of the 2-parameter inverse Lomax distribution.

### Usage

    invlomax(link.scale = "loge", link.p = "loge",
             earg.scale=list(), earg.p=list(),
             init.scale = NULL, init.p = 1, zero = NULL)

### Arguments

`link.scale, link.p` | Parameter link functions applied to the (positive) scale parameter `scale` and (positive) shape parameter `p`. See `Links` for more choices.
`earg.scale, earg.p` | List. Extra argument for each of the links. See `earg` in `Links` for general information.
`init.scale, init.p` | Optional initial values for `scale` and `p`.
`zero` | An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. Here, the values must be from the set {1,2} which correspond to `scale`, `p`, respectively.

### Details

The 2-parameter inverse Lomax distribution is the 4-parameter generalized beta II distribution with shape parameters a=q=1. It is also the 3-parameter Dagum distribution with shape parameter a=1, as well as the beta distribution of the second kind with q=1. More details can be found in Kleiber and Kotz (2003).

The inverse Lomax distribution has density

f(y) = p y^(p-1) / [b^p (1 + y/b)^(p+1)]

for b > 0, p > 0, y > 0. Here, b is the scale parameter `scale`, and `p` is a shape parameter. The mean does not seem to exist.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, and `vgam`.

### Note

If the self-starting initial values fail, try experimenting with the initial value arguments, especially those whose default value is not `NULL`.

### Author(s)

T. W. Yee

### References

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

### See Also

`Invlomax`, `genbetaII`, `betaII`, `dagum`, `sinmad`, `fisk`, `lomax`, `paralogistic`, `invparalogistic`.

### Examples

    y = rinvlomax(n=2000, 6, 2)
    fit = vglm(y ~ 1, invlomax, trace=TRUE)
    fit = vglm(y ~ 1, invlomax, trace=TRUE, crit="c")
    coef(fit, mat=TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 0.7-9 Index]