paralogistic {VGAM} | R Documentation |
Maximum likelihood estimation of the 2-parameter paralogistic distribution.
paralogistic(link.a = "loge", link.scale = "loge", earg.a = list(), earg.scale = list(), init.a = 1, init.scale = NULL, zero = NULL)
link.a, link.scale |
Parameter link functions applied to the
(positive) shape parameter |
earg.a, earg.scale |
List. Extra argument for each of the links.
See |
init.a, init.scale |
Optional initial values for |
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
|
The 2-parameter paralogistic distribution is the 4-parameter generalized beta II distribution with shape parameter p=1 and a=q. It is the 3-parameter Singh-Maddala distribution with a=q. More details can be found in Kleiber and Kotz (2003).
The 2-parameter paralogistic has density
f(y) = a^2 y^(a-1) / [b^a (1 + (y/b)^a)^(1+a)]
for a > 0, b > 0, y > 0.
Here, b is the scale parameter scale
,
and a is the shape parameter.
The mean is
E(Y) = b gamma(1 + 1/a) gamma(a - 1/a) / gamma(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.
Paralogistic
,
genbetaII
,
betaII
,
dagum
,
fisk
,
invlomax
,
lomax
,
invparalogistic
.
pdat = data.frame(y = rparalogistic(n = 3000, 4, 6)) fit = vglm(y ~ 1, paralogistic, pdat, trace = TRUE) fit = vglm(y ~ 1, paralogistic(init.a = 2.3, init.sc = 5), pdat, trace = TRUE, crit = "c") coef(fit, matrix = TRUE) Coef(fit) summary(fit)