dF1 {SubTS}

Pdf for f_1

Description

Evaluates the pdf f_1(x) intruduced in Grabchak (2021).

Usage

dF1(x, a, p)

Arguments

x

Vector of real numbers.

a

Parameter >=0.

p

Parameter >1.

Details

Evaluates the pdf

f_1(x) = exp(-x^p)*x^(-1-a)/K_1, x>1

where K_1 is a normalizing constant. This is distribution is needed to simulate p-RDTS random variables.

Value

Returns a vector of real numbers corresponding to the values of f_1(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 = (10:20)/10
  dF1(x, .5, 2)