Distribution function and quantile function
of the generalized logistic distribution.
Usage
cdfglo(x, para = c(0, 1, 0))
quaglo(f, para = c(0, 1, 0))
Value
cdfglo gives the distribution function;
quaglo gives the quantile function.
Arguments
x
Vector of quantiles.
f
Vector of probabilities.
para
Numeric vector containing the parameters of the distribution,
in the order \(\xi, \alpha, k\) (location, scale, shape).
Details
The generalized logistic distribution with
location parameter \(\xi\),
scale parameter \(\alpha\) and
shape parameter \(k\) has distribution function
$$F(x)=1/\lbrace 1+\exp(-y)\rbrace$$ where
$$y=-k^{-1}\log\lbrace1-k(x-\xi)/\alpha\rbrace,$$
with \(x\) bounded by \(\xi+\alpha/k\)
from below if \(k<0\) and from above if \(k>0\),
and quantile function
$$x(F)=\xi+{\alpha\over k}\biggl\lbrace1-\biggl({1-F \over F}\biggr)^k\biggr\rbrace.$$
The logistic distribution is the special case \(k=0\).
See Also
cdfkap for the kappa distribution,
which generalizes the generalized logistic distribution.