1d:T7e2,# 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. ```r 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 ```r ## 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.

Parameter_Conversion_Nolan_pm1_pm0 function