Generalized Logistic Distribution — GenLogistic • anyFit

Three-parameter Generalised Logistic distribution with location $\mu$, scale $\sigma$, and shape $\xi$. Density, distribution, and quantile functions are provided via the lmomco package. The distribution encompasses symmetric ($\xi = 0$) and asymmetric forms and is used in regional frequency analysis of hydrological extremes. Fitting is performed via closed-form L-moments through pelglo.

Define $z = (x - \mu)/\sigma$. The probability density function is: $$f(x) = \frac{1}{\sigma} \frac{e^{-z}}{(1+e^{-z})^2}, \quad \xi = 0$$ $$f(x) = \frac{1}{\sigma} \frac{(1-\xi z)^{1/\xi-1}}{(1+(1-\xi z)^{1/\xi})^2}, \quad \xi \neq 0$$ where:

$\mu$ — location parameter (location)
$\sigma$ — scale parameter (scale)
$\xi$ — shape parameter (shape)

Usage

dgenlogi(x, location, scale, shape)

pgenlogi(q, location, scale, shape)

qgenlogi(p, location, scale, shape)

Arguments

x, q: vector of quantiles.
location: location parameter.
scale: scale parameter.
shape: shape parameter.
p: vector of probabilities.