inv.lomax: Inverse Lomax Distribution Family Function

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/family.actuary.R

Description

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

Usage

1
2
3
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 >= 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

1
2
3
4
5
6
7
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)

Example output

Loading required package: stats4
Loading required package: splines
VGLM    linear loop  1 :  loglikelihood = -10346.0237
VGLM    linear loop  2 :  loglikelihood = -10346.0192
VGLM    linear loop  3 :  loglikelihood = -10346.0192
VGLM    linear loop  1 :  coefficients = 2.79976273, 0.38282768
VGLM    linear loop  2 :  coefficients = 2.333349295, 0.731457743
VGLM    linear loop  3 :  coefficients = 2.174806691, 0.871736357
VGLM    linear loop  4 :  coefficients = 2.147124033, 0.895404231
VGLM    linear loop  5 :  coefficients = 2.145902682, 0.896373509
VGLM    linear loop  6 :  coefficients = 2.145872449, 0.896395146
VGLM    linear loop  7 :  coefficients = 2.145871720, 0.896395663
VGLM    linear loop  8 :  coefficients = 2.145871702, 0.896395676
VGLM    linear loop  9 :  coefficients = 2.145871702, 0.896395676
            loge(scale) loge(shape2.p)
(Intercept)    2.145872      0.8963957
   scale shape2.p 
8.549491 2.450754 

Call:
vglm(formula = y ~ 1, family = inv.lomax(iscale = exp(3)), data = idata, 
    trace = TRUE, epsilon = 1e-08, crit = "coef")


Pearson residuals:
                   Min      1Q  Median     3Q     Max
loge(scale)     -1.378 -0.9121 -0.0466 0.8319 11.5122
loge(shape2.p) -17.152  0.1785  0.3115 0.3934  0.4253

Coefficients: 
              Estimate Std. Error z value Pr(>|z|)    
(Intercept):1  2.14587    0.10398   20.64   <2e-16 ***
(Intercept):2  0.89640    0.07716   11.62   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Number of linear predictors:  2 

Names of linear predictors: loge(scale), loge(shape2.p)

Log-likelihood: -10346.02 on 3998 degrees of freedom

Number of iterations: 9 

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.