calcShockArrivalIntensities: Calculate the shock-arrival intensities

In hsloot/rmo: A package for the Marshall-Olkin distribution

Calculate the shock-arrival intensities

Description

Calculates the shock-arrival intensities, the distribution parameter for rmo().

Usage

calcShockArrivalIntensities(object, d, cscale = 1, ...)

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

rmo()

Other Bernstein function generics: calcExShockArrivalIntensities(), calcExShockSizeArrivalIntensities(), calcIterativeDifference(), calcMDCMGeneratorMatrix(), calcValue(), getDefaultMethodString(), getLevyDensity(), getStieltjesDensity()

Examples

bf <- AlphaStableBernsteinFunction(alpha = 0.7)
calcShockArrivalIntensities(bf, 3)

hsloot/rmo documentation built on May 1, 2024, 4:28 a.m.