aw2k {FatTailsR}

Local Conversion Functions Between Kiener Distribution Parameters

Description

Conversion functions between parameters a, k, w, d, e used in Kiener distributions K2, K3 and K4.

Usage

aw2k(a, w)

aw2d(a, w)

aw2e(a, w)

ad2e(a, d)

ad2k(a, d)

ad2w(a, d)

ae2d(a, e)

ae2k(a, e)

ae2w(a, e)

ak2d(a, k)

ak2e(a, k)

ak2w(a, k)

de2a(d, e)

de2k(d, e)

de2w(d, e)

dk2a(d, k)

dk2e(d, k)

dk2w(d, k)

dw2a(d, w)

dw2e(d, w)

dw2k(d, w)

ek2a(e, k)

ek2d(e, k)

ek2w(e, k)

ew2a(e, w)

ew2d(e, w)

ew2k(e, w)

kd2a(k, d)

kd2e(k, d)

kd2w(k, d)

ke2a(k, e)

ke2d(k, e)

ke2w(k, e)

kw2a(k, w)

kw2d(k, w)

kw2e(k, w)

Arguments

a

a numeric value.

w

a numeric value.

d

a numeric value.

e

a numeric value.

k

a numeric value.

Details

a (alpha) is the left tail parameter, w (omega) is the right tail parameter, d (delta) is the distortion parameter, e (epsilon) is the eccentricity parameter. k (kappa) is the harmonic mean of a and w and describes a global tail parameter. They are defined by:

aw2k(a, w) = k = 2 / (1/a + 1/w) = \frac{2}{\frac{1}{a} +\frac{1}{w}}

aw2d(a, w) = d = (-1/a + 1/w) / 2 = \frac{-\frac{1}{a} +\frac{1}{w}}{2}

aw2e(a, w) = e = (a - w) / (a + w) = \frac{a-w}{a+w}

kd2a(k, d) = a = 1 / ( 1/k - d) = \frac{1}{\frac{1}{k} - d}

kd2w(k, d) = w = 1 / ( 1/k + d) = \frac{1}{\frac{1}{k} + d}

ke2a(k, e) = a = k / (1 - e) = \frac{k}{1-e}

ke2w(k, e) = w = k / (1 + e) = \frac{k}{1+e}

ke2d(k, e) = d = e / k = \frac{e}{k}

kd2e(k, d) = e = k * d

de2k(k, e) = k = e / d = \frac{e}{d}

See Also

The asymmetric Kiener distributions K2, K3, K4: kiener2, kiener3, kiener4

Examples

aw2k(4, 6); aw2d(4, 6); aw2e(4, 6)
outer(1:6, 1:6, aw2k)