cdfglo: Generalized logistic distribution

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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 Oct. 1, 2024, 1:08 a.m.