Parameter_Conversion {stable}

Easy conversion of parameters between stabledist (Nolan 1-parameterization) and stable (Lambert and Lindsey 1999)

Description

sd2s has stabledist parameter (Nolan 1-parameterization) inputs and returns stable parameters as put forth in Lambert and Lindsey (1999) and used in this package. s2sd has stable parameter (Lambert and Lindsey (1999)) inputs and returns stabledist parameters (Nolan 1-parameterization). See examples and the readme. There's also more context and references in '?stable::dstable'.

Usage

sd2s(alpha, beta, gamma, delta, pm = 1)

s2sd(tail, skew, disp, loc, pm = 1)

Arguments

alpha

the stabledist 'alpha'

beta

the stabledist 'beta'

gamma

the stabledist 'gamma'

delta

the stabledist 'delta'

pm

default 1; currently only value supported. the stabledist parameterization 'pm'

tail

the stable 'tail' analogous to 'alpha'

skew

the stable 'skew' analogous to 'beta'

disp

the stable 'disp' analogous to 'gamma'

loc

the stable 'loc' analogous to 'delta'

Details

[Swihart 2022 update:] See the examples and README for how to make equivalent calls to those of 'stabledist' (i.e., Nolan's 1-parameterization as detailed in Nolan (2020)) using these functions and this package. See github for Lambert and Lindsey 1999 JRSS-C journal article, which details the parameterization of the Buck (1995) stable distribution which allowed a Fourier inversion to arrive at a form of the $g_d$ function as detailed in Nolan (2020), The Buck (1995) parameterization most closely resembles the Zolotarev B parameterization outlined in Definition 3.6 on page 93 of Nolan (2020) – except that Buck (1995) did not allow the scale parameter to multiply with the location parameter. This explains why the 'Zolotarev B' entry in Table 3.1 on page 97 of Nolan (2020) has the location parameter being multiplied by the scale parameter whereas in converting the Lindsey and Lambert (1999) to Nolan 1-parameterization the location parameter stays the same.

Value

sd2s returns stable parameters as put forth in Lambert and Lindsey (1999) and used in this package. s2sd returns stabledist parameters (Nolan 1-parameterization).

References

Lambert, P. and Lindsey, J.K. (1999) Analysing financial returns using regression models based on non-symmetric stable distributions. Applied Statistics, 48, 409-424.

Nolan, John P. Univariate stable distributions. Berlin/Heidelberg, Germany: Springer, 2020.

Examples

## Not run: 
q <- -1
# nolan pm=1 parameters:
a <-  1.3
b <-  -0.4
c <-  2
d <-  0.75
s <- sd2s(alpha=a, beta=b, gamma=c, delta=d)
stable::pstable(q, tail = s$tail, skew=s$skew, disp = s$disp, loc  = s$loc)
stabledist::pstable(q, alpha=a, beta=b , gamma=c , delta=d, pm=1)
sd <- s2sd(tail = s$tail, skew=s$skew, disp = s$disp, loc  = s$loc)
stabledist::pstable(q, alpha=sd$alpha, beta=sd$beta , gamma=sd$gamma , delta=sd$delta, pm=1)
## End(Not run)