Calculates the shock-arrival intensities, the intensities parameter for
rmo().
Arguments
- object
An object deriving from the class BernsteinFunction.
- d
A positive integer, larger than two, for the dimension.
- cscale
A positive number for the composite scaling factor.
- ...
pass-through parameter.
Details
For a given Bernstein function, the shock-arrival intensities are defined as $$ \lambda_{I} = {(-1)}^{{\lvert I\rvert}-1} \Delta^{{\lvert I\rvert}}{ \psi{(d-{\lvert I\rvert})} } , \quad 1 \leq {\lvert I\rvert} \leq d . $$ The calculation of the shock-arrival intensities using this formula is usually not numerically stable. Consequently, the various alternative approaches are used dependent on the class of the Bernstein function.
The following binary representation is used to map subsets \(I\) of \({\{1, \ldots, d\}}\) to an integers \(0, \ldots, 2^d-1\): $$ I \equiv \sum_{k \in I}{ 2^{k-1} } . $$
See also
Other Bernstein function generics:
defaultMethod(),
exIntensities(),
exQMatrix(),
levyDensity(),
stieltjesDensity(),
uexIntensities(),
valueOf(),
valueOf0()
Examples
bf <- AlphaStableBernsteinFunction(alpha = 0.7)
intensities(bf, 3)
#> [1] 0.53316449 0.53316449 0.09134031 0.53316449 0.09134031 0.09134031 0.28415490