Parameter_Conversion_Nolan_pm1_pm0 function

Easy conversion of parameters between stabledist Nolan 1-parameterization and 0-parameterization

pm0_to_pm1 has stabledist parameter inputs for pm=0 and returns pm=1 equivalent parameterization. pm1_to_pm0 has stabledist parameter inputs for pm=1 and returns pm=0 equivalent parameterization.

pm0_to_pm1(a0, b0, c0, d0)

pm1_to_pm0(a1, b1, c1, d1)

Arguments

• a0: the stabledist 'alpha' for pm=0 in 'stabledist'
• b0: the stabledist 'beta' for pm=0 in 'stabledist'
• c0: the stabledist 'gamma' for pm=0 in 'stabledist'
• d0: the stabledist 'delta' for pm=0 in 'stabledist'
• a1: the stabledist 'alpha' for pm=1 in 'stabledist'
• b1: the stabledist 'beta' for pm=1 in 'stabledist'
• c1: the stabledist 'gamma' for pm=1 in 'stabledist'
• d1: the stabledist 'delta' for pm=1 in 'stabledist'

Returns

pm0_to_pm1 has stabledist parameter inputs for pm=0 and returns pm=1 equivalent parameterization. pm1_to_pm0 has stabledist parameter inputs for pm=1 and returns pm=0 equivalent parameterization.

Details

See table Table 3.1 on page 97 of Nolan (2020).

Examples

## Not run:
q <- -1
# nolan pm=1 parameters:
a1 <-  1.3
b1 <-  -0.4
c1 <-  2
d1 <-  0.75
# Convert to nolan pm=0 parameters:
pm0 <- pm1_to_pm0(a1,b1,c1,d1)
a0 <- pm0$a0
b0 <- pm0$b0
c0 <- pm0$c0
d0 <- pm0$d0
# check:
stabledist::pstable(q, alpha=a1, beta=b1 , gamma=c1 , delta=d1, pm=1)
#> [1] 0.1965513
# only change delta=d0 for pm=0
stabledist::pstable(q, alpha=a1, beta=b1 , gamma=c1 , delta=d0, pm=0)
stabledist::pstable(q, alpha=a0, beta=b0 , gamma=c0 , delta=d0, pm=0)
#> [1] 0.1965513
stabledist::dstable(q, alpha=a1, beta=b1 , gamma=c1 , delta=d1, pm=1)
#> [1] 0.0572133
# only change delta=d0 for pm=0
stabledist::dstable(q, alpha=a1, beta=b1 , gamma=c1 , delta=d0, pm=0)
stabledist::dstable(q, alpha=a0, beta=b0 , gamma=c0 , delta=d0, pm=0)
#> [1] 0.0572133
## End(Not run)

References

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