dSubCTS {SubTS}

PDF of CTS subordinator

Description

Evaluates the pdf of the classical tempered stable (CTS) subordinator. When alpha=0 this is the pdf of the gamma distribution.

Usage

dSubCTS(x, alpha, c, ell)

Arguments

x

Vector of real numbers.

alpha

Parameter in [0,1).

c

Parameter >0

ell

Tempering parameter >0

Details

Returns the pdf of a classical tempered stable subordinator. The distribution has Laplace transform

L(z) = exp( c int_0^infty (e^(-xz)-1)e^(-x/ell) x^(-1-alpha) dx), z>0

and Levy measure

M(dx) = c e^(-x/ell) x^(-1-alpha) 1(x>0)dx.

Value

Returns a vector of real numbers corresponding to the values of pdf.

Note

Uses the method dtweedie in the Tweedie package.

Author(s)

Michael Grabchak and Lijuan Cao

References

M. Grabchak (2016). Tempered Stable Distributions: Stochastic Models for Multiscale Processes. Springer, Cham.

Examples

  x = (0:20)/10
  dSubCTS(x, .5, 1, 1.5)