lomax {VGAM} | R Documentation |
Maximum likelihood estimation of the 2-parameter Lomax distribution.
lomax(link.scale = "loge", link.q = "loge", earg.scale=list(), earg.q=list(), init.scale = NULL, init.q = 1, zero = NULL)
link.scale, link.q |
Parameter link function applied to the
(positive) parameters scale and q .
See Links for more choices.
|
earg.scale, earg.q |
List. Extra argument for each of the links.
See earg in Links for general information.
|
init.scale, init.q |
Optional initial values for scale and q .
|
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 , q , respectively.
|
The 2-parameter Lomax distribution is the 4-parameter generalized beta II distribution with shape parameters a=p=1. It is probably more widely known as the Pareto (II) distribution. It is also the 3-parameter Singh-Maddala distribution with shape parameter a=1, as well as the beta distribution of the second kind with p=1. More details can be found in Kleiber and Kotz (2003).
The Lomax distribution has density
f(y) = q / [b (1 + y/b)^(1+q)]
for b > 0, q > 0, y > 0.
Here, b is the scale parameter scale
,
and q
is a shape parameter.
The cumulative distribution function is
F(y) = 1 - [1 + (y/b)]^(-q).
The mean is
E(Y) = b/(q-1)
provided q > 1.
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.
Lomax
,
genbetaII
,
betaII
,
dagum
,
sinmad
,
fisk
,
invlomax
,
paralogistic
,
invparalogistic
.
y = rlomax(n=2000, 6, 2) fit = vglm(y ~ 1, lomax, trace=TRUE) fit = vglm(y ~ 1, lomax, trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) summary(fit)