mixbox (version 1.2.3)

rigaussian: Simulating from inversse Gaussian random variable.

Description

Using method of Michael and Schucany (1976), we can generate from inversse Gaussian random variable. The density function of an inversse Gaussian distribution is given by $$ f_W(w\vert{\bold{\theta}}) =\sqrt{\frac{\beta}{2 \pi w^3}}\exp\biggl\{-\frac{\beta(w - \alpha)^2}{2\alpha^2 w}\biggr\},$$ where \(w>0\) and \({\bold{\theta}}=(\alpha, \beta)^{\top}\). Herein \(\alpha>0\) is the mean and \(\beta> 0\) are the first (mean) and second (shape) parameter of this family, respectively.

Usage

rigaussian(n, alpha, beta)

Value

simulated realizations of size \(n\) from inversse Gaussian random variable.

Arguments

n

size of required samples.

alpha

tail mean parameter.

beta

shape parameter.

Author

Mahdi Teimouri

References

J. R. Michael and Schucany, (1976). Generating Random Variates Using Transformations with Multiple Roots, The American Statistician, 30(2), 88-90, tools:::Rd_expr_doi("10.1080/00031305.1976.10479147").

Examples

# \donttest{
    n <- 100
alpha <- 4
 beta <- 2
rigaussian(n, alpha, beta)
# }