genbetaII {VGAM} | R Documentation |
Maximum likelihood estimation of the 4-parameter generalized beta II distribution.
genbetaII(link.a = "loge", link.scale = "loge", link.p = "loge", link.q = "loge", earg.a=list(), earg.scale=list(), earg.p=list(), earg.q=list(), init.a = NULL, init.scale = NULL, init.p = 1, init.q = 1, zero = NULL)
link.a, link.scale, link.p, link.q |
Parameter link functions applied to the
shape parameter a ,
scale parameter scale ,
shape parameter p , and
shape parameter q .
All four parameters are positive.
See Links for more choices.
|
earg.a, earg.scale, earg.p, earg.q |
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 .
A NULL means a value is computed internally.
|
init.p, init.q |
Optional initial values for p 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 {1,2,3,4} which correspond to
a , scale , p , q , respectively.
|
This distribution is most useful for unifying a substantial number of size distributions. For example, the Singh-Maddala, Dagum, Fisk (log-logistic), Lomax (Pareto type II), inverse Lomax, beta distribution of the second kind distributions are all special cases. Full details can be found in Kleiber and Kotz (2003), and Brazauskas (2002).
The 4-parameter generalized beta II distribution has density
f(y) = a y^(ap-1) / [b^(ap) B(p,q) (1 + (y/b)^a)^(p+q)]
for a > 0, b > 0, p > 0, q > 0, y > 0.
Here B is the beta function, and
b is the scale parameter scale
,
while the others are shape parameters.
The mean is
E(Y) = b gamma(p + 1/a) gamma(q - 1/a) / ( gamma(p) gamma(q))
provided -ap < 1 < aq.
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
.
Successful convergence depends on having very good initial values. This is rather difficult for this distribution! More improvements could be made here.
T. W. Yee
Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ: Wiley-Interscience.
Brazauskas, V. (2002) Fisher information matrix for the Feller-Pareto distribution. Statistics & Probability Letters, 59, 159–167.
lino
,
betaff
,
betaII
,
dagum
,
sinmad
,
fisk
,
lomax
,
invlomax
,
paralogistic
,
invparalogistic
.
y = rsinmad(n=3000, 4, 6, 2) # Not very good data! fit = vglm(y ~ 1, genbetaII, trace=TRUE) fit = vglm(y ~ 1, genbetaII(init.p=1.0, init.a=4, init.sc=7, init.q=2.3), trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) summary(fit)