dF2 {SubTS}

Pdf for f_2

Description

Evaluates the pdf f_2(x) intruduced in Grabchak (2021).

Usage

dF2(x, a, p)

Arguments

x

Vector of real numbers.

a

Parameter in [0,1).

p

Parameter >1.

Details

Evaluates the pdf

f_2(x) = (exp(-x^p) - exp(-x))*x^(-1-a)/K_2, 0<x<1

where K_2 is a normalizing constant. This distribution is needed to simulate p-RDTS random variables.

Value

Returns a vector of real numbers corresponding to the values of f_2(x).

Author(s)

Michael Grabchak and Lijuan Cao

References

M. Grabchak (2021). An exact method for simulating rapidly decreasing tempered stable distributions. Statistics and Probability Letters, 170: Article 109015.

Examples

  x = (0:10)/10
  dF2(x, .5, 1.5)