| cdfglo {lmom} | R Documentation |
Generalized logistic distribution
Description
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))
Arguments
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
Numeric vector containing the parameters of the distribution,
in the order |
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.
Value
cdfglo gives the distribution function;
quaglo gives the quantile function.
Note
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
See Also
cdfkap for the kappa distribution,
which generalizes the generalized logistic distribution.
Examples
# Random sample from the generalized logistic distribution
# with parameters xi=0, alpha=1, k=-0.5.
quaglo(runif(100), c(0,1,-0.5))