# aw2k: Local Conversion Functions Between Kiener Distribution... In FatTailsR: Kiener Distributions and Fat Tails in Finance

## Description

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

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 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}

The asymmetric Kiener distributions K2, K3, K4: kiener2, kiener3, kiener4
 1 2 aw2k(4, 6); aw2d(4, 6); aw2e(4, 6) outer(1:6, 1:6, aw2k)