Class for linear Bernstein functions

A linear Bernstein function is a Bernstein function with only a drift, i.e., \(a = 0\) and \(\nu = 0\). In particular, $$ \psi(x) = b x, x > 0. $$

Slots

scale

The nonnegative drift parameter (i.e. \(b\) in the representation).

See also

calcIterativeDifference(), calcShockArrivalIntensities(), calcExShockArrivalIntensities(), calcExShockSizeArrivalIntensities(), calcMDCMGeneratorMatrix(), rextmo(), rpextmo()

Other Bernstein function classes: AlphaStableBernsteinFunction-class, BernsteinFunction-class, CompleteBernsteinFunction-class, CompositeScaledBernsteinFunction-class, ConstantBernsteinFunction-class, ConvexCombinationOfBernsteinFunctions-class, ExponentialBernsteinFunction-class, GammaBernsteinFunction-class, InverseGaussianBernsteinFunction-class, LevyBernsteinFunction-class, ParetoBernsteinFunction-class, PoissonBernsteinFunction-class, ScaledBernsteinFunction-class, SumOfBernsteinFunctions-class

Other Bernstein function boundary classes: ConstantBernsteinFunction-class, PoissonBernsteinFunction-class

Examples

# Create an object of class LinearBernsteinFunction
LinearBernsteinFunction()
#> An object of class "LinearBernsteinFunction"
#> 	 (invalid or not initialized)
LinearBernsteinFunction(scale = 0.2)
#> An object of class "LinearBernsteinFunction"
#> - scale: 0.2

# Evaluate the Bernstein function
bf <- LinearBernsteinFunction(scale = 0.3)
calcIterativeDifference(bf, 1:5)
#> [1] 0.3 0.6 0.9 1.2 1.5

# Calculate shock-arrival intensities
bf <- LinearBernsteinFunction(scale = 0.8)
calcShockArrivalIntensities(bf, 3)
#> [1] 0.8 0.8 0.0 0.8 0.0 0.0 0.0

# Calculate exchangeable shock-arrival intensities
bf <- LinearBernsteinFunction(scale = 0.4)
calcExShockArrivalIntensities(bf, 3)
#> [1] 0.4 0.0 0.0

# Calculate exchangeable shock-size arrival intensities
bf <- LinearBernsteinFunction(scale = 0.2)
calcExShockSizeArrivalIntensities(bf, 3)
#> [1] 0.6 0.0 0.0

# Calculate the Markov generator
bf <- LinearBernsteinFunction(scale = 0.6)
calcMDCMGeneratorMatrix(bf, 3)
#>      [,1] [,2] [,3]         [,4]
#> [1,] -1.8  1.8  0.0 2.220446e-16
#> [2,]  0.0 -1.2  1.2 2.220446e-16
#> [3,]  0.0  0.0 -0.6 6.000000e-01
#> [4,]  0.0  0.0  0.0 0.000000e+00