logisst: The Standardized Logistic Distribution

In FatTailsR: Kiener Distributions and Fat Tails in Finance and Neuroscience

The Standardized Logistic Distribution

Description

Density, distribution function, quantile function, random generation, value-at-risk, left-tail mean, right-tail mean, expected shortfall for the standardized logistic distribution, equivalent to dpqrlogis(..., scale = g*sqrt(3)/pi).

Usage

dlogisst(x, m = 0, g = 1, log = FALSE)

plogisst(q, m = 0, g = 1, lower.tail = TRUE, log.p = FALSE)

qlogisst(p, m = 0, g = 1, lower.tail = TRUE, log.p = FALSE)

rlogisst(n, m = 0, g = 1)

dplogisst(p, m = 0, g = 1, log = FALSE)

dqlogisst(p, m = 0, g = 1, k = 3.2, log = FALSE)

llogisst(x, m = 0, g = 1)

dllogisst(lp, m = 0, g = 1, k = 3.2, log = FALSE)

qllogisst(lp, m = 0, g = 1, k = 3.2, lower.tail = TRUE)

varlogisst(p, m = 0, g = 1, k = 3.2, lower.tail = TRUE,
  log.p = FALSE)

ltmlogisst(p, m = 0, g = 1, lower.tail = TRUE, log.p = FALSE)

rtmlogisst(p, m = 0, g = 1, lower.tail = TRUE, log.p = FALSE)

eslogisst(p, m = 0, g = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

x	vector of quantiles.
m	numeric. a central parameter (also used in model K1, K2, K3 and K4).
g	numeric. a scale parameter (also used in model K1, K2, K3 and K4).
log	boolean.
q	vector of quantiles.
lower.tail	logical. If TRUE, use p. If FALSE, use 1-p.
log.p	logical. If TRUE, probabilities p are given as log(p).
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
k	numeric. The tail parameter, preferably strictly positive. Can be a vector (see details).
lp	vector of logit of probabilities.

Details

dlogisst function (log is available) is defined for x in (-Inf, +Inf) by:

dlogisst(x, m, g) = stats::dlogis(x, location = m, scale = g*sqrt(3)/pi)

plogisst function is defined for q in (-Inf, +Inf) by:

plogisst(q, m, g) = stats::plogis(q, location = m, scale = g*sqrt(3)/pi)

qlogisst function is defined for p in (0, 1) by:

qlogisst(p, m, g) = stats::qlogis(p, location = m, scale = g*sqrt(3)/pi)

rlogisst function generates n random values.

In addition to the classical formats, the prefixes dp, dq, l, dl, ql are also provided:

dplogisst function (log is available) is defined for p in (0, 1) by:

dplogisst(p, m, g) = p*(1-p)/g*pi/sqrt(3) + m*0

dqlogisst function (log is available) is defined for p in (0, 1) by:

dqlogisst(p, m, g) = 1/p/(1-p)*sqrt(3)/pi*g + m*0

llogisst function is defined for x in (-Inf, +Inf) by:

llogisst(x, m, g) = (x-m)/g*pi/sqrt(3)

dllogisst function is defined for lp = logit(p) in (-Inf, +Inf) by :

dllogisst(lp, m, g) = p*(1-p)/g*pi/sqrt(3)

qllogisst function is defined for lp = logit(p) in (-Inf, +Inf) by :

qllogisst(lp, m, g) = m + sqrt(3)/pi*g

If k is a vector, then the use of the function outer is recommanded.

Functions eslogis is the expected shortfall of the logistic function (times a factor 2). When p<=0.5, it is equivalent (times -1) to the left tail mean ltmlogisst. When p>0.5, it is equivalent to the right tail mean rtmlogisst. ltmlogisst and rtmlogisst are used to calculate the h parameter in hkiener1, hkiener2, hkiener3, hkiener4.

See Also

Kiener distribution K1 kiener1 which has location (m) and scale (g) parameters.

FatTailsR documentation built on June 8, 2025, 11:34 a.m.