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

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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

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

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