rmo: A package for simulating Marshall–Olkin distributions

The rmo-package provides efficient sampling algorithms for the Marshall–Olkin distribution and a flexible S4-class system for creating diverse parametrizations.

Sampling

Simulation algorithms are provided for various MO parametrizations. The semantic naming scheme r*mo is used, e.g.,

• rpextmo() allows to simulate from parametric families of extendible Marshall–Olkin distributions. The function takes a killing-rate, a drift, a scaling factor, a parameter vector, and a family name as input.

• rextmo() allows to simulate from extendible Marshall–Olkin distributions. It takes a Bernstein function as input.

• rexmo() allows to simulate from exchangeable Marshall–Olkin distributions. It takes a vector of exchangeable shock-size arrival intensities as input.

• rmo() allows to simulate from Marshall–Olkin distributions. It takes vector of shock arrival intensities as input and uses the Arnold model or exogenous shock model for sampling; the former can be used up until dimension \(30\), but the latter should only be used in very small dimensions.

The default simulation algorithm is the Markovian death-counting model. Dependent on the parametrization, other algorithms can be used, e.g., the exogenous shock model, the Arnold model, or the Lévy-frailty model.

Bernstein functions

A Bernstein function can be used to parametrize the extendible Marshall–Olkin distribution.

• Many families of Bernstein functions are available, e.g. ParetoBernsteinFunction, ExponentialBernsteinFunction, and AlphaStableBernsteinFunction.

• Bernstein functions can be recombined by scaling, by summation or by composition, which can be used to create new Bernstein functions with ScaledBernsteinFunction, CompositeScaledBernsteinFunction and SumOfBernsteinFunctions.

• An object that derives from BernsteinFunction can be used to generate the Marshall–Olkin shock arrival intensities with calcShockArrivalIntensities(). It can be used to generate (scaled) exchangeable shock-size arrival intensities with calcExShockSizeArrivalIntensities().

See also

Useful links:

• https://github.com/hsloot/rmo

• Report bugs at https://github.com/hsloot/rmo/issues

Author

Maintainer: Henrik Sloot henrik.sloot@gmail.com (ORCID)