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

## Description

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`.

## Usage

 ```1 2 3``` ```stableMode(alpha, beta, beta.max = 1 - 1e-11, tol = .Machine\$double.eps^0.25) ```

## Arguments

 `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()`.

## Value

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

## Author(s)

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

For definition and the “dpqr”-functions, `StableDistribution`, also for the references.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## 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))) } ```