ckiener1234 {FatTailsR}

Quantile (VaR) and Expected Shortfall Corrective Functions

Description

Quantile functions (or VaR) and Expected Shortfall of Kiener distributions K1, K2, K3 and K4, usually calculated at pprobs2 = c(0.01, 0.025, 0.05, 0.95, 0.975, 0.99), can be expressed as:

1. Quantile of the logit function multiplied by a fat tail (c)orrective function ckiener1234;

2. Expected s(h)ortfall of the logistic function multiplied by a corrective function hkiener1234.

Both functions ckiener1234 and hkiener1234 are independant from the scale parameter g and are indirect measures of the tail curvature. A value close to 1 indicates a model similar to the logistic function with almost no curvature and probably parameter k > 8. When k (or a,w) decreases, the values of c and h increase and indicate some more pronounced symmetric or asymmetric curvature, depending on values of d,e. Note that if (min(a,k,w) <= 1), ckiener1234 still exists but the expected shortfall and hkiener1234 become undefined (NA).

Some financial applications use threshold values on ckiener1234 or hkiener1234 to select or discard stocks over time as they become less or more risky.

Usage

hkiener1(p, m = 0, g = 1, k = 3.2, lower.tail = TRUE, log.p = FALSE)

hkiener2(p, m = 0, g = 1, a = 3.2, w = 3.2, lower.tail = TRUE,
  log.p = FALSE)

hkiener3(p, m = 0, g = 1, k = 3.2, d = 0, lower.tail = TRUE,
  log.p = FALSE)

hkiener4(p, m = 0, g = 1, k = 3.2, e = 0, lower.tail = TRUE,
  log.p = FALSE)

hkiener7(p, coefk = c(0, 1, 3.2, 3.2, 3.2, 0, 0), lower.tail = TRUE,
  log.p = FALSE)

ckiener1(p, k = 3.2, lower.tail = TRUE, log.p = FALSE)

ckiener2(p, a = 3.2, w = 3.2, lower.tail = TRUE, log.p = FALSE)

ckiener3(p, k = 3.2, d = 0, lower.tail = TRUE, log.p = FALSE)

ckiener4(p, k = 3.2, e = 0, lower.tail = TRUE, log.p = FALSE)

ckiener7(p, coefk = c(0, 1, 3.2, 3.2, 3.2, 0, 0), lower.tail = TRUE,
  log.p = FALSE)

Arguments

p

numeric or vector of probabilities.

m

numeric. parameter m used in model K1, K2, K3 and K4.

g

numeric. parameter g used in model K1, K2, K3 and K4.

k

numeric. parameter k used in model K1, 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).

a

numeric. parameter a used in model K2.

w

numeric. parameter w used in model K2.

d

numeric. parameter d used in model K3.

e

numeric. parameter e used in model K4.

coefk

vector or 7 columns-matrix representing parameters c(m,g,a,k,w,d,e) obtained from paramkienerX.

See Also

logit, qkiener1, qkiener2, qkiener3, qkiener4, fitkienerX.