# cdfglo: Generalized logistic distribution In lmom: L-Moments

 cdfglo 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 \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.

### 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))


lmom documentation built on Aug. 29, 2023, 9:07 a.m.