stableMode: Mode of the Stable Distribution Function
In stabledist: Stable Distribution Functions

Description Usage Arguments Value Author(s) See Also Examples

Computes the mode of the stable distribution, i.e., the maximum of its density function in the "0" parametrization, i.e., the maximum x_0 of dstable(x, alpha, beta, gamma = 1, delta = 0, pm = 0).

Finds the maximum of dstable numerically, using optimize.

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stableMode(alpha, beta,
           beta.max = 1 - 1e-11,
           tol = .Machine$double.eps^0.25)

`alpha, beta`	numeric parameters: value of the index parameter `alpha` in the range (0,2], and the skewness parameter `beta`, in the range [-1, 1].
`beta.max`	for numerical purposes, values of beta too close to 1, are set to `beta.max`. Do not modify unless you know what you're doing.
`tol`	numerical tolerance for `optimize()`.

returns a numeric value, the location of the stable mode.

Diethelm Wuertz for the Rmetrics R-port; minor cleanup by Martin Maechler.

For definition and the “dpqr”-functions, StableDistribution, also for the references.

## beta = 0  <==>  symmetric  <==>  mode = 0
all.equal(stableMode(alpha=1, beta=0), 0)
al.s <- c(1e-100, seq(0,2, by = 1/32)[-1])
stopifnot(vapply(al.s, function(alp)
                 stableMode(alpha=alp, beta=0), 1.) == 0)

## more interesting: asymmetric (beta != 0):
stableMode(alpha=1.2, beta=0.1)

if(stabledist:::doExtras()) { # takes 2.5 seconds
 sm0.5 <- vapply(al.s, function(AA)
                 stableMode(alpha=AA, beta= 0.5), 1.)
 plot(al.s, sm0.5, type = "o", col=2, xlab = quote(alpha), ylab="mode",
      main = quote("Mode of stable"*{}(alpha, beta == 0.5, pm==0)))
}