Calculate the values for a Bernstein function and its higher-order, alternating iterated forward differences, possibly scaled by a binomial coefficient, i.e., $$ \binom{n}{k} {(-1)}^{j-1} \Delta^{j}{ \psi(c x) } , \quad x > 0 . $$ The evaluation of Bernstein functions using this formula is usually not numerically stable. Consequently, the various alternative approaches are used dependent on the class of the Bernstein function.
Arguments
- object
An object deriving from the class BernsteinFunction.
- x
A nonnegative numeric vector at which the iterated difference of the Bernstein function is evaluated.
- difference_order
A nonnegative integer with the order of the alternating iterated forward differences taken on the Bernstein function.
- n, k
Nonnegative numbers for the binomial factor.
- cscale
A positive number for the composite scaling factor.
- ...
Pass-through parameter.
See also
Other Bernstein function generics:
defaultMethod(),
exIntensities(),
exQMatrix(),
intensities(),
levyDensity(),
stieltjesDensity(),
uexIntensities(),
valueOf0()
Examples
bf <- AlphaStableBernsteinFunction(alpha = 0.7)
valueOf(bf, 1:5)
#> [1] 1.000000 1.624505 2.157669 2.639016 3.085169