yulesimon {VGAM} | R Documentation |
Yule-Simon Family Function
Description
Estimating the shape parameter of the Yule-Simon distribution.
Usage
yulesimon(lshape = "loglink", ishape = NULL, nsimEIM = 200,
zero = NULL)
Arguments
lshape |
Link function for the shape parameter,
called
|
ishape |
Optional initial value for the (positive) parameter.
See |
nsimEIM , zero |
See |
Details
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,\ldots
.
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.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
and vgam
.
Author(s)
T. W. Yee
References
Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, 425–440.
See Also
Examples
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)