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)