yulesimon {VGAM} | R Documentation |
Estimating the shape parameter of the Yule-Simon distribution.
yulesimon(lshape = "loglink", ishape = NULL, nsimEIM = 200, zero = NULL)
lshape |
Link function for the shape parameter,
called
rho below.
See |
ishape |
Optional initial value for the (positive) parameter.
See |
nsimEIM, zero |
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.
The distribution was named after Udny Yule and Herbert A. Simon. Simon originally called it the Yule distribution. This family function can handle multiple responses.
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, shape = exp(1.5 - x2))) with(ydata, table(y)) fit <- vglm(y ~ x2, yulesimon, data = ydata, trace = TRUE) coef(fit, matrix = TRUE) summary(fit)