Differenced Zeta Distribution Family Function
Estimates the parameter of the differenced zeta distribution.
diffzeta(start = 1, lshape = "loglink", ishape = NULL)
lshape, ishape |
Same as |
start |
Smallest value of the support of the distribution. Must be a positive integer. |
The PMF is
P(Y=y) = (a/y)^(s) - / (a/(1+y))^(s), s>0, y=a,a+1,...,
where s is the positive shape parameter, and a is start.
According to Moreno-Sanchez et al. (2016), this model
fits quite well to about 40 percent of all the English books in the
Project Gutenberg data base (about 30,000 texts).
Multiple responses are handled.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
T. W. Yee
Moreno-Sanchez, I., Font-Clos, F. and Corral, A. (2016). Large-Scale Analysis of Zipf's Law in English Texts, PLoS ONE, 11(1), 1–19.
odata <- data.frame(x2 = runif(nn <- 1000)) # Artificial data odata <- transform(odata, shape = loglink(-0.25 + x2, inverse = TRUE)) odata <- transform(odata, y1 = rdiffzeta(nn, shape)) with(odata, table(y1)) ofit <- vglm(y1 ~ x2, diffzeta, data = odata, trace = TRUE, crit = "coef") coef(ofit, matrix = TRUE)
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