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 Links for more choices and for general information.
|
irho |
Optional initial value for the (positive) parameter.
See CommonVGAMffArguments for more information.
The default is to obtain an initial value internally. Use this argument
if the default fails.
|
nsimEIM |
See CommonVGAMffArguments for more information.
|
The probability function is
f(y;rho) = rho*beta(y,rho+1),
where the parameter rho>0
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.
x = runif(n <- 1000) y = ryules(n, rho=exp(1.5-x)) table(y) fit = vglm(y ~ x, yulesimon, trace=TRUE) coef(fit, matrix=TRUE) summary(fit)