gig {qbld}

Generalised Inverse Gaussian

Description

Probability distribution function, random generation for the Generalised Inverse Gaussian with three parameters a(chi), b(psi), p.

Usage

dgig(x, a, b, p, log_density)

rgig(n, lambda, a, b)

Arguments

x

: Argument of pdf

a

: chi parameter. Must be nonnegative for positive lambda and positive else.

b

: psi parameter. Must be nonnegative for negative lambda and positive else.

log_density

: logical; returns log density if TRUE

n

: number of observations

lambda, p

: lambda parameter

Details

The Generalised Inverse Gaussian distrubtion(GIG), which has the following pdf

f(x) = x^{\lambda-1}\exp\{-\frac{\omega}{2}(x + \frac{1}{x})\}

Value

• rgig returns a vector of random numbers from GIG(a,b,p).

• dgig returns returns density of a GIG(a,b,p) at point x.

References

Devroye, L. Random variate generation for the generalized inverse Gaussian distribution. Stat Comput 24, 239–246 (2014).

Wolfgang Hörmann and Josef Leydold (2013). Generating generalized inverse Gaussian random variates, Statistics and Computing (to appear), DOI: 10.1007/s11222-013-9387-3

J. S. Dagpunar (1989). An easily implemented generalised inverse Gaussian generator, Comm. Statist. B – Simulation Comput. 18, 703–710.

See Also

raldmix for random sampling from Asymmetric Laplace distribution

Examples

rgig(n = 1, lambda = 0.5, a = 1, b = 2)
dgig(x = 1, a = 1, b = 2, p = 0.5, log_density = FALSE)