# inv.lomax: Inverse Lomax Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

 inv.lomax R Documentation

## Inverse Lomax Distribution Family Function

### Description

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

### Usage

``````inv.lomax(lscale = "loglink", lshape2.p = "loglink", 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 \geq 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`.

T. W. Yee

### References

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

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

### Examples

``````idata <- data.frame(y = rinv.lomax(2000, sc = 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)
``````

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.