dGGa {SubTS}

Pdf of the generalized gamma distribution

Description

Evaluates the pdf of the generalized gamma distribution.

Usage

dGGa(x, a, p, b)

Arguments

x

Vector of real numbers.

a

Parameter >0.

p

Parameter >0.

b

Parameter >0.

Details

Evaluates the pdf of the generalized gamma distribution with density

g(x) = exp(-b*x^p)*x^(a-1)/K_3, x>0,

where K_3 is a normalizing constant. This distribution is needed to simulate p-RDTS random variables with negative alpha values.

Value

Returns a vector of real numbers corresponding to the values of g(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.

E.W. Stacy (1962) A generalization of the gamma distribution. Annals of Mathematical Statistics, 33(3):1187-1192.

Examples

  x = (0:20)/10
  dGGa(x, 2.5, 1.5, 3.1)