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

Details

The generalized logistic distribution with location parameter xi, scale parameter alpha and shape parameter k has distribution function

F(x)= 1 / (1+exp(-y))

where

y = (-1/k) log(1-k(x-xi)/alpha) ,

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 (1 - ((1-F)/F)^k) / k .

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))

Results