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).
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)
vector of quantiles.
numeric. a central parameter (also used in model K1, K2, K3 and K4).
numeric. a scale parameter (also used in model K1, K2, K3 and K4).
boolean.
vector of quantiles.
logical. If TRUE, use p. If FALSE, use 1-p.
logical. If TRUE, probabilities p are given as log(p).
vector of probabilities.
number of observations. If length(n) > 1, the length is taken to be the number required.
numeric. The tail parameter, preferably strictly positive. Can be a vector (see details).
vector of logit of probabilities.
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.
Kiener distribution K1 kiener1 which has
location (m) and scale (g) parameters.