yulesimon {VGAM} | R Documentation |
Estimating the parameter of the Yule-Simon distribution.
yulesimon(link = "loge", earg = list(), irho = NULL, nsimEIM = 200)
link, earg |
Link function and extra argument for the rho parameter.
See |
irho |
Optional initial value for the (positive) parameter.
See |
nsimEIM |
See |
The probability function is
f(y;rho) = rho*beta(y,rho+1),
where the parameter rho>0,
beta is the beta
function,
and y=1,2,....
The function dyules
computes this probability function.
The mean of Y, which is returned as fitted values, is
rho/(rho-1)
provided rho > 1.
The variance of Y is
rho^2/((rho-1)^2 (rho-2))
provided rho > 2.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
T. W. Yee
Simon, H. A. (1955) On a class of skew distribution functions. Biometrika, 42, 425–440.
ydata = data.frame(x2 = runif(nn <- 1000)) ydata = transform(ydata, y = ryules(nn, rho = exp(1.5-x2))) with(ydata, table(y)) fit = vglm(y ~ x2, yulesimon, ydata, trace = TRUE) coef(fit, matrix = TRUE) summary(fit)