VGAM (version 0.9-4)

invlomax: Inverse Lomax Distribution Family Function

Description

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

Usage

invlomax(lscale = "loge", lshape2.p = "loge",
         iscale = NULL, ishape2.p = 1, zero = NULL)

Arguments

lscale, lshape2.p

Parameter link functions applied to the (positive) scale parameter scale and (positive) shape parameter p. See Links for more choices.

iscale, ishape2.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.

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 exist; NAs are returned as the fitted values.

References

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

See Also

Invlomax, genbetaII, betaII, dagum, sinmad, fisk, lomax, paralogistic, invparalogistic, simulate.vlm.

Examples

idata <- data.frame(y = rinvlomax(n = 2000, exp(2), exp(1)))
fit <- vglm(y ~ 1, invlomax, data = idata, trace = TRUE)
fit <- vglm(y ~ 1, invlomax(iscale = exp(2), ishape2.p = exp(1)), data = idata,
            trace = TRUE, epsilon = 1e-8)
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)