logit: Logit and Invlogit Functions

In FatTailsR: Kiener Distributions and Fat Tails in Finance

Logit and Invlogit Functions

Description

The logit and invlogit functions, widely used in this package, are wrappers of qlogis and plogis functions.

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 ltmlogis. When p>0.5, it is equivalent to the right tail mean rtmlogis. ltmlogis and rtmlogis are used to calculate the h parameter in hkiener1, hkiener2, hkiener3, hkiener4.

Usage

logit(p)

invlogit(x)

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

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

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

Arguments

p	numeric. one value or a vector between 0 and 1.
x	numeric. one value or a vector of numerics.
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).
lower.tail	logical. If TRUE, use p. If FALSE, use 1-p.
log.p	logical. If TRUE, probabilities p are given as log(p).

Details

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

logit(p) = log( p/(1-p) )

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

invlogit(x) = exp(x)/(1+exp(x)) = plogis(x)

Examples

    
logit( c(ppoints(11, a = 1), NA, NaN) )
invlogit( c(-Inf, -10:10, +Inf, NA, NaN) )

FatTailsR documentation built on May 29, 2024, 1:33 a.m.