UnivRNG (version 1.2.3)

draw.inverse.gaussian: Generates variation from inverse Gaussian distribution

Description

This function implements pseudo-random number generation for an inverse Gaussian distribution with pdf

$$f(x|\mu,\lambda)=(\frac{\lambda}{2\pi})^{1/2}x^{-3/2}e^{-\frac{\lambda(x-\mu)^2}{2\mu^2x}}$$

for \(x > 0\), \(\mu > 0\), and \(\lambda > 0\) where \(\mu\) and \(\lambda\) are the location and scale parameters, respectively.

Usage

draw.inverse.gaussian(nrep,mu,lambda)

Arguments

nrep

Number of data points to generate.

mu

Location parameter for the desired inverse Gaussian distribution.

lambda

Scale parameter for the desired inverse Gaussian distribution.

Value

A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.

References

Michael, J. R., William, R. S., & Haas, R. W. (1976). Generating random variates using transformations with multiple roots. The American Statistician, 30, 88-90.

Examples

# NOT RUN {
draw.inverse.gaussian(nrep=100000,mu=1,lambda=1)

draw.inverse.gaussian(nrep=100000,mu=3,lambda=1)
# }