| hzeta {VGAM} | R Documentation |
Estimating the parameter of Haight's Zeta function.
hzeta(link = "loglog", earg=list(), init.alpha = NULL)
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.
|
init.alpha |
Optional initial value for the (positive) parameter.
The default is to obtain an initial value internally. Use this argument
if the default fails.
|
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 470 of Johnson N. L., Kotz S. and Kemp, A. W. (1993) Univariate Discrete Distributions, 2nd edition, Volume 2, New York: Wiley.
alpha = exp(exp(0.5)) # 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 fitted(fit)[1:4,]