R: Inverse Lomax Distribution Family Function

inv.lomax {VGAM} | R Documentation

## Inverse Lomax Distribution Family Function

### Description

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

### Usage

    inv.lomax(lscale = "loge", lshape2.p = "loge", iscale = NULL,
        ishape2.p = NULL, imethod = 1, gscale = exp(-5:5),
        gshape2.p = exp(-5:5), probs.y = c(0.25, 0.5, 0.75), zero = "shape2.p")

### Arguments

`lscale, lshape2.p` | Parameter link functions applied to the (positive) parameters b, and p. See `Links` for more choices.
`iscale, ishape2.p, imethod, zero` | See `CommonVGAMffArguments` for information. For `imethod = 2` a good initial value for `ishape2.p` is needed to obtain a good estimate for the other parameter.
`gscale, gshape2.p` | See `CommonVGAMffArguments` for information.
`probs.y` | See `CommonVGAMffArguments` for information.

### 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; the median is returned as the fitted values. This family function handles multiple responses.

### Value

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

### Note

See the notes in `genbetaII`.

### 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

`inv.lomax`, `genbetaII`, `betaII`, `dagum`, `sinmad`, `fisk`, `lomax`, `paralogistic`, `inv.paralogistic`, `simulate.vlm`.

### Examples

    idata <- data.frame(y = rinv.lomax(n = 2000, scale = exp(2), exp(1)))
    fit <- vglm(y ~ 1, inv.lomax, data = idata, trace = TRUE)
    fit <- vglm(y ~ 1, inv.lomax(iscale = exp(3)), data = idata,
                trace = TRUE, epsilon = 1e-8, crit = "coef")
    coef(fit, matrix = TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 1.0-3 Index]