SubTS (version 1.0)

dSubCTS: 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)

Value

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

Arguments

x

Vector of real numbers.

alpha

Parameter in [0,1).

c

Parameter >0

ell

Tempering parameter >0

Author

Michael Grabchak and Lijuan Cao

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.

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)