logff {VGAM} | R Documentation |
Estimating the parameter of the logarithmic distribution.
logff(link = "logit", earg=list(), init.c = NULL)
link |
Parameter link function applied to the parameter c,
which lies between 0 and 1.
See Links for more choices.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
init.c |
Optional initial value for the c parameter.
If given, it often pays to start with a larger value, e.g., 0.95.
The default is to choose an initial value internally.
|
The logarithmic distribution is based on the logarithmic series, and is scaled to a probability function. Its probability function is f(y) = a * c^y / y, for y=1,2,3,..., where 0 < c < 1, and a = -1 / log(1-c). The mean is a*c/(1-c) (returned as the fitted values) and variance is a*c*(1-a*c)/(1-c)^2.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
The function log
computes the natural logarithm.
In the VGAM library, a link function with option
loge
corresponds to this.
T. W. Yee
Chapter 7 of Johnson N. L., Kemp, A. W. and Kotz S. (2005) Univariate Discrete Distributions, 3rd edition, Hoboken, New Jersey: Wiley.
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.
y = rlog(n=1000, prob=logit(0.2, inverse=TRUE)) fit = vglm(y ~ 1, logff, trace=TRUE, crit="c") coef(fit, matrix=TRUE) Coef(fit) ## Not run: hist(y, prob=TRUE, breaks=seq(0.5, max(y)+0.5, by=1)) x = seq(1, max(y), by=1) lines(x, dlog(x, Coef(fit)[1]), col="red", type="h") ## End(Not run)