| fisk {VGAM} | R Documentation |
Maximum likelihood estimation of the 2-parameter Fisk distribution.
fisk(link.a = "loge", link.scale = "loge",
earg.a=list(), earg.scale=list(),
init.a = NULL, init.scale = NULL, zero = NULL)
link.a, link.scale |
Parameter link functions applied to the
(positive) parameters a and scale.
See Links for more choices.
|
earg.a, earg.scale |
List. Extra argument for each of the links.
See earg in Links for general information.
|
init.a, init.scale |
Optional initial values for a and scale.
|
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
a, scale, respectively.
|
The 2-parameter Fisk (aka log-logistic) distribution is the 4-parameter generalized beta II distribution with shape parameter q=p=1. It is also the 3-parameter Singh-Maddala distribution with shape parameter q=1, as well as the Dagum distribution with p=1. More details can be found in Kleiber and Kotz (2003).
The Fisk distribution has density
f(y) = a y^(a-1) / [b^a (1 + (y/b)^a)^2]
for a > 0, b > 0, y > 0.
Here, b is the scale parameter scale,
and a is a shape parameter.
The cumulative distribution function is
F(y) = 1 - [1 + (y/b)^a]^(-1) = [1 + (y/b)^(-a)]^(-1).
The mean is
E(Y) = b gamma(1 + 1/a) gamma(1 - 1/a)
provided a > 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.
Fisk,
genbetaII,
betaII,
dagum,
sinmad,
invlomax,
lomax,
paralogistic,
invparalogistic.
y = rfisk(n=200, 4, 6) fit = vglm(y ~ 1, fisk, trace=TRUE) fit = vglm(y ~ 1, fisk(init.a=3.3), trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) summary(fit)