VGAM (version 1.0-4)

# inv.lomax: 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.

## Value

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

## 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.

## 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

Run this code
```# NOT RUN {
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)
# }
```

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