hzeta {VGAM} | R Documentation |
Estimating the parameter of Haight's Zeta function.
hzeta(link = "loglog", earg=list(), ialpha = NULL, nsimEIM=100)
link |
Parameter link function for the parameter.
See Links for more choices.
Here, a log-log link keeps the parameter greater than one, meaning
the mean is finite.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
ialpha |
Optional initial value for the (positive) parameter.
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) = (2y-1)^(-alpha) - (2y+1)^(-alpha),
where the parameter alpha>0
and y=1,2,....
The function dhzeta
computes this probability function.
The mean of Y, which is returned as fitted values, is
(1-2^(-alpha))*zeta(alpha)
provided alpha > 1, where zeta is
Riemann's zeta function.
The mean is a decreasing function of alpha.
The mean is infinite if alpha <= 1, and
the variance is infinite if alpha <= 2.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
T. W. Yee
Page 533 of Johnson N. L., Kemp, A. W. and Kotz S. (2005) Univariate Discrete Distributions, 3rd edition, Hoboken, New Jersey: Wiley.
alpha = exp(exp(-0.1)) # The parameter y = rhzeta(n=1000, alpha) # Generate some hzeta random variates fit = vglm(y ~ 1, hzeta, trace = TRUE, crit="c") coef(fit, matrix=TRUE) Coef(fit) # Useful for intercept-only models; should be same as alpha c(mean(y), fitted(fit)[1,]) summary(fit)