Paralogistic Distribution Family Function
Maximum likelihood estimation of the 2-parameter paralogistic distribution.
paralogistic(lscale = "loglink", lshape1.a = "loglink", iscale = NULL,
ishape1.a = NULL, imethod = 1, lss = TRUE, gscale = exp(-5:5),
gshape1.a = seq(0.75, 4, by = 0.25), probs.y = c(0.25, 0.5, 0.75),
zero = "shape")lss |
See |
lshape1.a, lscale |
Parameter link functions applied to the
(positive) parameters a and |
iscale, ishape1.a, imethod, zero |
See |
gscale, gshape1.a |
See |
probs.y |
See |
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; these are returned as the fitted values. This family function handles multiple responses.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
See the notes in genbetaII.
T. W. Yee
Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.
pdata <- data.frame(y = rparalogistic(n = 3000, exp(1), scale = exp(1)))
fit <- vglm(y ~ 1, paralogistic(lss = FALSE), data = pdata, trace = TRUE)
fit <- vglm(y ~ 1, paralogistic(ishape1.a = 2.3, iscale = 5),
data = pdata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.