invlomax {VGAM} | R Documentation |
Maximum likelihood estimation of the 2-parameter inverse Lomax distribution.
invlomax(link.scale = "loge", link.p = "loge", earg.scale=list(), earg.p=list(), init.scale = NULL, init.p = 1, zero = NULL)
link.scale, link.p |
Parameter link functions applied to the
(positive) scale parameter scale and
(positive) shape parameter p .
See Links for more choices.
|
earg.scale, earg.p |
List. Extra argument for each of the links.
See earg in Links for general information.
|
init.scale, init.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.
|
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.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
If the self-starting initial values fail, try experimenting
with the initial value arguments, especially those whose
default value is not NULL
.
T. W. Yee
Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ: Wiley-Interscience.
Invlomax
,
genbetaII
,
betaII
,
dagum
,
sinmad
,
fisk
,
lomax
,
paralogistic
,
invparalogistic
.
y = rinvlomax(n=2000, 6, 2) fit = vglm(y ~ 1, invlomax, trace=TRUE) fit = vglm(y ~ 1, invlomax, trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) summary(fit)