betaII {VGAM} | R Documentation |
Maximum likelihood estimation of the 3-parameter beta II distribution.
betaII(link.scale = "loge", link.p = "loge", link.q = "loge", earg.scale=list(), earg.p=list(), earg.q=list(), init.scale = NULL, init.p = 1, init.q = 1, zero = NULL)
link.scale, link.p, link.q |
Parameter link functions applied to the
(positive) parameters scale , p and q .
See Links for more choices.
|
earg.scale, earg.p, earg.q |
List. Extra argument for each of the links.
See earg in Links for general information.
|
init.scale, init.p, init.q |
Optional initial values for scale , 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} which correspond to
scale , p , q , respectively.
|
The 3-parameter beta II is the 4-parameter generalized beta II distribution with shape parameter a=1. It is also known as the Pearson VI distribution. Other distributions which are special cases of the 3-parameter beta II include the Lomax (p=1) and inverse Lomax (q=1). More details can be found in Kleiber and Kotz (2003).
The beta II distribution has density
f(y) = y^(p-1) / [b^p B(p,q) (1 + y/b)^(p+q)]
for b > 0, p > 0, q > 0, y > 0.
Here, b is the scale parameter scale
,
and the others are shape parameters.
The mean is
E(Y) = b gamma(p + 1) gamma(q - 1) / ( gamma(p) gamma(q))
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.
betaff
,
genbetaII
,
dagum
,
sinmad
,
fisk
,
invlomax
,
lomax
,
paralogistic
,
invparalogistic
.
y = rsinmad(n=2000, a=1, 6, 2) # Not genuine data! fit = vglm(y ~ 1, betaII, trace=TRUE) fit = vglm(y ~ 1, betaII(init.p=0.7, init.q=0.7), trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) summary(fit)